Enumerate all Keychain items in my iOS application

SecItemCopyMatching is the right call for that. First we build our query dictionary so that the items' attributes are returned in dictionaries, and that all items are returned:

NSMutableDictionary *query = [NSMutableDictionary dictionaryWithObjectsAndKeys:
    (__bridge id)kCFBooleanTrue, (__bridge id)kSecReturnAttributes,
    (__bridge id)kSecMatchLimitAll, (__bridge id)kSecMatchLimit,
    nil];

As SecItemCopyMatching requires at least the class of the returned SecItems, we create an array with all the classes…

NSArray *secItemClasses = [NSArray arrayWithObjects:
                           (__bridge id)kSecClassGenericPassword,
                           (__bridge id)kSecClassInternetPassword,
                           (__bridge id)kSecClassCertificate,
                           (__bridge id)kSecClassKey,
                           (__bridge id)kSecClassIdentity,
                           nil];

...and for each class, set the class in our query, call SecItemCopyMatching, and log the result.

for (id secItemClass in secItemClasses) {
    [query setObject:secItemClass forKey:(__bridge id)kSecClass];

    CFTypeRef result = NULL;
    SecItemCopyMatching((__bridge CFDictionaryRef)query, &result);
    NSLog(@"%@", (__bridge id)result);
    if (result != NULL) CFRelease(result);
}

In production code, you should check that the OSStatus returned by SecItemCopyMatching is either errSecItemNotFound (no items found) or errSecSuccess (at least one item was found).

Swift 3+ version that returns also the keys (kSecAttrAccount):

open func getAllKeyChainItemsOfClass(_ secClass: String) -> [String:String] {

        let query: [String: Any] = [
            kSecClass : secClass,
            kSecReturnData  : kCFBooleanTrue,
            kSecReturnAttributes : kCFBooleanTrue,
            kSecReturnRef : kCFBooleanTrue,
            kSecMatchLimit : kSecMatchLimitAll
        ]

        var result: AnyObject?

        let lastResultCode = withUnsafeMutablePointer(to: &result) {
            SecItemCopyMatching(query as CFDictionary, UnsafeMutablePointer($0))
        }

        var values = [String:String]()
        if lastResultCode == noErr {
            let array = result as? Array<Dictionary<String, Any>>

            for item in array! {
                if let key = item[kSecAttrAccount] as? String, 
                   let value = item[kSecValueData] as? Data {
                   values[key] = String(data: value, encoding:.utf8) 
                }
            }
        }

        return values
    }

A Swift 4 update to @Cosmin's Swift 3 answer.

open func getAllKeyChainItemsOfClass(_ secClass: String) -> [String:String] {
    let query: [String: Any] = [
        kSecClass as String : secClass,
        kSecReturnData as String  : kCFBooleanTrue,
        kSecReturnAttributes as String : kCFBooleanTrue,
        kSecReturnRef as String : kCFBooleanTrue,
        kSecMatchLimit as String: kSecMatchLimitAll
    ]
                
    var result: AnyObject?
                
    let lastResultCode = withUnsafeMutablePointer(to: &result) {
        SecItemCopyMatching(query as CFDictionary, UnsafeMutablePointer($0))
    }
                
    var values = [String:String]()
    if lastResultCode == noErr {
        let array = result as? Array<Dictionary<String, Any>>
                    
        for item in array! {
            if let key = item[kSecAttrAccount as String] as? String,
               let value = item[kSecValueData as String] as? Data {
                   values[key] = String(data: value, encoding:.utf8)
             }
         }
    }
                
    return values
}