Which standard objects don't support triggers?

Following Standard objects don't support trigger, I have gathered so far as of Spring' 17 release.

• AcceptedEventRelation
• AccountContactRelation
• AccountCleanInfo
• AccountContactRole
• AccountFeed
• AccountHistory
• AccountOwnerSharingRule
• AccountPartner
• AccountShare
• AccountTag
• AccountTeamMember
• AccountTerritoryAssignmentRule
• AccountTerritoryAssignmentRuleItem
• AccountTerritorySharingRule
• ActionLinkGroupTemplate
• ActionLinkTemplate
• ActivityHistory
• AdditionalNumber
• AllowedEmailDomain
• Announcement
• ApexClass
• ApexComponent
• ApexLog
• ApexPage
• ApexTestQueueItem
• ApexTestResult
• ApexTestResultLimits
• ApexTestRunResult
• ApexTestSuite
• ApexTrigger
• AppMenuItem
• Approval
• Article Type__DataCategorySelection
• Article Type__Feed
• AssetFeed
• AssetOwnerSharingRule
• AssetShare
• AssetTag
• AssignedResource
• AssignmentRule
• AsyncApexJob
• AttachedContentDocument
• AttachedContentNote
• AuraDefinition
• AuraDefinitionBundle
• AuthConfig
• AuthConfigProviders
• AuthProvider
• AuthSession
• BackgroundOperation
• BackgroundOperationResult
• Bookmark
• BrandTemplate
• BusinessHours
• BusinessProcess
• CallCenter
• CampaignFeed
• CampaignInfluence
• CampaignInfluenceModel
• CampaignMemberStatus
• CampaignOwnerSharingRule
• CampaignShare
• CampaignTag
• CaseArticle
• CaseContactRole
• CaseFeed
• CaseHistory
• CaseMilestone
• CaseOwnerSharingRule
• CaseShare
• CaseSolution
• CaseStatus
• CaseTag
• CaseTeamMember
• CaseTeamRole
• CaseTeamTemplate
• CaseTeamTemplateMember
• CaseTeamTemplateRecord
• CategoryData
• CategoryNode
• CategoryNodeLocalization
• ChatterActivity
• ChatterAnswersReputationLevel
• ChatterConversation
• ChatterConversationMember
• ChatterMessage
• ClientBrowser
• CollaborationGroupFeed
• CollaborationGroupMemberRequest
• CollaborationGroupRecord
• CollaborationInvitation
• CombinedAttachment
• Community (Zone)
• ConnectedApplication
• ContactCleanInfo
• ContactFeed
• ContactHistory
• ContactOwnerSharingRule
• ContactShare
• ContactTag
• ContentAsset
• ContentDistributionView
• ContentDocumentFeed
• ContentDocumentHistory
• ContentFolder
• ContentFolderItem
• ContentFolderLink
• ContentFolderMember
• ContentHubItem
• ContentHubRepository
• ContentNote
• ContentVersionHistory
• ContentWorkspace
• ContentWorkspaceDoc
• ContractContactRole
• ContractFeed
• ContractHistory
• ContractHistory
• ContractLineItemHistory
• ContractStatus
• ContractTag
• CorsWhitelistEntry
• CronJobDetail
• CronTrigger
• CurrencyType
• CustomBrand
• CustomBrandAsset
• Custom Object__Feed
• CustomPermission
• CustomPermissionDependency
• DandBCompany
• Dashboard
• DashboardComponent
• DashboardComponentFeed
• DashboardFeed
• DashboardTag
• DataAssessmentFieldMetric
• DataAssessmentMetric
• DataAssessmentValueMetric
• DatacloudCompany
• DatacloudContact
• DatacloudDandBCompany
• DatacloudOwnedEntity
• DatacloudPurchaseUsage
• DatacloudSocialHandle
• DatedConversionRate
• DcSocialProfile
• DcSocialProfileHandle
• DeclinedEventRelation
• Division
• DivisionLocalization
• Document
• DocumentAttachmentMap
• DocumentTag
• Domain
• DomainSite
• DuplicateRule
• EmailDomainKey
• EmailMessageRelation
• EmailServicesAddress
• EmailServicesFunction
• EmailStatus
• EmailTemplate
• EmbeddedServiceDetail
• EntitlementFeed
• EntitlementHistory
• EntitlementTemplate
• EntityHistory
• EntityMilestone
• EntitySubscription
• EnvironmentHubMember
• EventFeed
• EventLogFile
• Lightning Error Event Type
• Lightning Interaction Event Type
• Lightning Page View Event Type
• Lightning Performance Event Type
• Login Event Type — LOGIN_STATUS Values
• EventRelation
• EventTag
• EventWhoRelation
• ExternalDataSource
• ExternalDataUserAuth
• FeedAttachment
• FeedLike
• FeedPollChoice
• FeedPollVote
• FeedPost
• FeedRevision
• FeedTrackedChange
• FieldHistoryArchive
• FieldPermissions
• FiscalYearSettings
• FlexQueueItem
• FlowInterview
• FlowInterviewOwnerSharingRule
• FlowInterviewShare
• Folder
• FolderedContentDocument
• ForecastingAdjustment
• ForecastingFact
• ForecastingItem
• ForecastingOwnerAdjustment
• ForecastingQuota
• ForecastingType
• ForecastingUserPreference
• ForecastShare
• Goal
• GoalFeed
• GoalHistory
• GoalLink
• GoalShare
• GoogleDoc
• Group
• GroupMember
• HashtagDefinition
• Holiday
• IdeaReputation
• IdeaReputationLevel
• IdeaTheme
• KnowledgeableUser
• KnowledgeArticle
• KnowledgeArticleVersion
• KnowledgeArticleVersionHistory
• KnowledgeArticleViewStat
• KnowledgeArticleVoteStat
• LeadCleanInfo
• LeadFeed
• LeadHistory
• LeadOwnerSharingRule
• LeadShare
• LeadStatus
• LeadTag
• LimitAllocationPerApp
• LineitemOverride
• LinkedArticleFeed
• LinkedArticleHistory
• ListView
• ListViewChart
• ListViewChartInstance
• LiveAgentSessionHistory
• LiveAgentSessionOwnerSharingRule
• LiveAgentSessionShare
• LiveChatBlockingRule
• LiveChatButton
• LiveChatButtonDeployment
• LiveChatButtonSkill
• LiveChatDeployment
• LiveChatSensitiveDataRule
• LiveChatTranscriptHistory
• LiveChatTranscriptOwnerSharingRule
• LiveChatTranscriptShare
• LiveChatTranscriptSkill
• LiveChatUserConfig
• LiveChatUserConfigProfile
• LiveChatUserConfigUser
• LoginEvent
• LoginGeo
• LoginHistory
• LoginIp
• LookedUpFromActivity
• MacroInstruction
• MailmergeTemplate
• MatchingRule
• MatchingRuleItem
• MetadataPackage
• MetadataPackageVersion
• Metric
• MetricDataLink
• MetricDataLinkHistory
• MetricFeed
• MetricHistory
• MetricsDataFile
• MetricShare
• MilestoneType
• Name
• NamedCredential
• NavigationLinkSet
• NavigationMenuItem
• NavigationMenuItemLocalization
• Network
• NetworkActivityAudit
• NetworkMember
• NetworkMemberGroup
• NetworkModeration
• NetworkPageOverride
• NetworkSelfRegistration
• NewsFeed
• OauthToken
• NoteAndAttachment
• NoteTag
• ObjectPermissions
• ObjectTerritory2AssignmentRule
• ObjectTerritory2AssignmentRuleItem
• ObjectTerritory2Association
• OpenActivity
• OperatingHours
• OperatingHoursFeed
• OperatingHoursHistory
• OpportunityCompetitor
• OpportunityContactRole
• OpportunityFeed
• OpportunityFieldHistory
• OpportunityHistory
• OpportunityLineItemSchedule
• OpportunityOverride
• OpportunityOwnerSharingRule
• OpportunityPartner
• OpportunityShare
• OpportunitySplitType
• OpportunityStage
• OpportunityTag
• OrderFeed
• OrderHistory
• OrderItemFeed
• OrderItemHistory
• OrderOwnerSharingRule
• Organization
• OrgWideEmailAddress
• OwnedContentDocument
• PackageLicense
• PackagePushError
• PackagePushJob
• PackagePushRequest
• PackageSubscriber
• PartnerNetworkConnection
• PartnerNetworkRecordConnection
• PartnerNetworkSyncLog
• PartnerRole
• Period
• PermissionSet
• PermissionSetAssignment
• PermissionSetLicense
• PermissionSetLicenseAssign
• PlatformAction
• PresenceUserConfig
• PresenceUserConfigProfile
• PresenceUserConfigUser
• Pricebook2History
• PricebookEntry
• ProcessDefinition
• ProcessInstance
• ProcessInstanceHistory
• ProcessInstanceStep
• ProcessInstanceNode
• ProcessInstanceWorkitem
• ProcessNode
• Product2Feed
• ProductEntitlementTemplate
• Profile
• ProfileSkillEndorsementFeed
• ProfileSkillEndorsementHistory
• ProfileSkillFeed
• ProfileSkillHistory
• ProfileSkillShare
• ProfileSkillUserFeed
• ProfileSkillUserHistory
• PushTopic
• QuantityForecast
• QuantityForecastHistory
• QueueRoutingConfig
• QuestionDataCategorySelection
• QuestionReportAbuse
• QuestionSubscription
• QueueSobject
• QuickTextHistory
• QuickTextOwnerSharingRule
• QuickTextShare
• QuoteDocument
• QuoteFeed
• RecentlyViewed
• RecordType
• RecordTypeLocalization
• ReplyReportAbuse
• Report
• ReportFeed
• ReportTag
• ReputationLevel
• ReputationLevelLocalization
• ReputationPointsRule
• ResourceAbsence
• ResourceAbsenceFeed
• ResourceAbsenceHistory
• RevenueForecast
• RevenueForecastHistory
• RuleTerritory2Association
• SamlSsoConfig
• Scontrol
• ScontrolLocalization
• SearchPromotionRule
• SecureAgent
• SecureAgentsCluster
• SecurityCustomBaseline (Beta)
• SelfServiceUser
• ServiceAppointment
• ServiceAppointmentFeed
• ServiceAppointmentHistory
• ServiceAppointmentOwnerSharingRule
• ServiceAppointmentShare
• ServiceChannel
• ServiceChannelStatus
• ServiceContractFeed
• ServiceContractHistory
• ServiceContractOwnerSharingRule
• ServiceContractShare
• ServicePresenceStatus
• ServiceResource
• ServiceResourceCapacity
• ServiceResourceCapacityFeed
• ServiceResourceCapacityHistory
• ServiceResourceFeed
• ServiceResourceHistory
• ServiceResourceOwnerSharingRule
• ServiceResourceShare
• ServiceResourceSkill
• ServiceResourceSkillFeed
• ServiceResourceSkillHistory
• ServiceTerritory
• ServiceTerritoryFeed
• ServiceTerritoryHistory
• ServiceTerritoryMember
• ServiceTerritoryMemberFeed
• ServiceTerritoryMemberHistory
• SessionPermSetActivation
• SetupAuditTrail
• SetupEntityAccess
• SignupRequest
• Site
• SiteDomain
• SiteHistory
• Skill
• SkillProfile
• SkillRequirement
• SkillRequirementFeed
• SkillRequirementHistory
• SkillUser
• SlaProcess
• SolutionFeed
• SolutionHistory
• SolutionStatus
• SolutionTag
• SOSDeployment
• SOSSession
• SOSSessionActivity
• SOSSessionHistory
• SOSSessionOwnerSharingRule
• SOSSessionShare
• Stamp
• StampAssignment
• StaticResource
• TagDefinition
• TaskFeed
• TaskPriority
• TaskRelation
• TaskStatus
• TaskTag
• TaskWhoRelation
• TenantSecret
• Territory2Model
• Territory2ModelHistory
• Territory2Type
• TestSuiteMembership
• ThirdPartyAccountLink
• TimeSlot
• TimeSlotHistory
• TopicFeed
• TopicLocalization—Beta
• TwoFactorInfo
• TwoFactorMethodsInfo
• TwoFactorTempCode
• UndecidedEventRelation
• UserAccountTeamMember
• UserAppInfo
• UserAppMenuCustomization
• UserAppMenuCustomizationShare
• UserAppMenuItem
• UserConfigTransferButton
• UserConfigTransferSkill
• UserCustomBadge
• UserCustomBadgeLocalization
• UserFeed
• UserLicense
• UserLogin
• UserMembershipSharingRule
• UserPackageLicense
• UserPreference
• UserProfile
• UserProfileFeed
• UserProvisioningConfig
• UserProvisioningRequestOwnerSharingRule
• UserProvisioningRequestShare
• UserRecordAccess
• UserRole
• UserShare
• UserTeamMember
• UserTerritory
• VerificationHistory
• VoiceCall
• VoiceCallList
• VoiceCallListItem
• VoiceCallListShare
• VoiceCallShare
• VoiceMailContent
• VoiceMailContentShare
• VoiceUserLine
• VoiceUserLineShare
• VoiceVendorInfo
• VoiceVendorLine
• VoiceVendorLineShare
• Vote
• WebLink
• WebLinkLocalization
• WorkAccess
• WorkAccessShare
• WorkBadgeDefinitionHistory
• WorkBadgeDefinitionShare
• WorkCoaching
• WorkCoachingFeed
• WorkCoachingHistory
• WorkCoachingShare
• WorkFeedback
• WorkFeedbackHistory
• WorkFeedbackQuestion
• WorkFeedbackQuestionHistory
• WorkFeedbackQuestionSet
• WorkFeedbackQuestionSetHistory
• WorkFeedbackQuestionSetShare
• WorkFeedbackQuestionShare
• WorkFeedbackRequest
• WorkFeedbackRequestFeed
• WorkFeedbackRequestHistory
• WorkFeedbackRequestShare
• WorkFeedbackShare
• WorkGoal
• WorkGoalCollaborator
• WorkGoalCollaboratorHistory
• WorkGoalFeed
• WorkGoalHistory
• WorkGoalLink
• WorkGoalShare
• WorkOrder
• WorkOrderFeed
• WorkOrderHistory
• WorkOrderLineItem
• WorkOrderLineItemFeed
• WorkOrderLineItemHistory
• WorkOrderShare
• WorkPerformanceCycle
• WorkPerformanceCycleFeed
• WorkPerformanceCycleHistory
• WorkPerformanceCycleShare
• WorkReward
• WorkRewardFund
• WorkRewardFundHistory
• WorkRewardFundShare
• WorkRewardFundType
• WorkRewardFundTypeHistory
• WorkRewardFundTypeShare
• WorkRewardHistory
• WorkRewardShare
• WorkThanksShare
• WorkType
• WorkTypeFeed
• WorkTypeHistory

UPDATED list, with a script to retrieve all non-triggerable objects on demand.

Run this and check the debug log to find out which standard objects are not triggerable:

Map<String, Schema.SObjectType> gd = Schema.getGlobalDescribe();
List<Schema.DescribeSObjectResult> standardObjDescs = new List<Schema.DescribeSObjectResult>();
for (Schema.SObjectType sobj : gd.values()) {
    Schema.DescribeSObjectResult sobjDesc = sobj.getDescribe();
    if (!sobjDesc.isCustom()) {
        standardObjDescs.add(sobjDesc);
    }
}

List<String> triggerableList = new List<String>();
List<String> NOTtriggerableList = new List<String>();
for (Schema.DescribeSObjectResult schemaDesc : standardObjDescs) {
    String sobjStruct = JSON.serialize(schemaDesc);
    DescribeSobjectResultJSON sobjProps = (DescribeSobjectResultJSON)JSON.deserialize(sobjStruct, DescribeSobjectResultJSON.class);
    if (sobjProps.triggerable) {
        triggerableList.add(sobjProps.name);
    } else {
        NOTtriggerableList.add(sobjProps.name);
    }
}
NOTtriggerableList.sort();
for (String notTrigble : NOTtriggerableList) {
    System.debug(notTrigble);
}

public class DescribeSobjectResultJSON { 
    public String name {get;set;}
    public Boolean triggerable {get;set;}
}

(I remembered that you can expose private object properties that the API doesn't expose via getters by serializing and deserializing, so you can run the following script that uses the triggerable property on Schema.DescribeSObjectResult to get the list.)

Add to @Santanu Boral 's helpful list:

• AggregateResult
• ApexEmailNotification
• ApexPageInfo
• AssetHistory
• AuraDefinitionBundleInfo
• AuraDefinitionInfo
• Community
• CustomObjectUserLicenseMetrics
• DataStatistics
• DataType
• DatacloudAddress
• EntityDefinition
• EntityParticle
• FieldDefinition
• ForecastingCategoryMapping
• ForecastingTypeToCategory
• GrantedByLicense
• InstalledMobileApp
• Knowledge__DataCategorySelection
• Knowledge__ViewStat
• Knowledge__VoteStat
• MacroShare
• OrderShare
• OwnerChangeOptionInfo
• PicklistValueInfo
• PlatformCachePartition
• PlatformCachePartitionType
• Publisher
• QuoteTemplateRichTextData
• RelationshipDomain
• RelationshipInfo
• SearchLayout
• SecureAgentPlugin
• SecureAgentPluginProperty
• SiteFeed
• StreamingChannelShare
• TenantUsageEntitlement
• Territory2ModelFeed
• TodayGoal
• TodayGoalShare
• TopicLocalization
• UserEntityAccess
• UserFieldAccess
• UserListView
• UserListViewCriterion

Though seeing how long this list is, it might make more sense to do a search than reference a comprehensive list...