What commands are counted as 'cheats'?

There are several commands that can be used in survival without cheats enabled. These generally are commands that do not have any effect on gameplay, hence you are not cheating.

Here is a list of the commands that can be operated without cheats:

/help - Displays help about other commands

/me - Writes a message relating to the player

/tell - Private message

/seed - Displays the world seed

/trigger - Can change enabled "trigger" type objectives

These commands do not require cheats, because they do not give the player any advantage. I think I have covered all the commands that are applicable to singleplayer, however I may have missed some. Let me know if I have.

I think you are looking for the "OP" commands, as listed on the Minecraft Wiki, under Commands. You are pretty much looking for any command listed as 'OP Only':

/achievementGives or removes an achievement from a player.
/banAdds player to banlist.
/ban-ip Adds IP address to banlist.
/banlist Displays banlist.
/blockdata Modifies the data tag of a block.
/clear Clears items from player inventory.
/clone Copies blocks from one place to another.
/debug Starts or stops a debugging session.
/defaultgamemode Sets the default game mode.
/deop Revoke operator status from a player.
/difficulty Sets the difficulty level.
/effect Add or remove status effects.
/enchant Enchants a player item.
/entitydata Modifies the data tag of an entity.
/execute Executes another command.
/fill Fills a region with a specific block.
/gamemode Sets a player's game mode.
/gamerule Sets or queries a game rule value.
/give Gives an item to a player.
/kick Kicks a player off a server.
/kill Kills entities (players, mobs, items, etc.).
/list Lists players on the server.
/op Grants operator status to a player.
/pardon Removes entries from the banlist.
/particle Creates particles.
/playsound Plays a sound.
/publish Opens single-player world to local network.
/replaceitem Replaces items in inventories.
/save-all Saves the server to disk.
/save-off Disables automatic server saves.
/save-on Enables automatic server saves.
/say Displays a message to multiple players.
/scoreboard Manages objectives, players, and teams.
/seed Displays the world seed.
/setblock Changes a block to another block.
/setidletimeout Sets the time before idle players are kicked.
/setworldspawn Sets the world spawn.
/spawnpoint Sets the spawn point for a player.
/spreadplayers Teleports entities to random locations.
/stats Update objectives from command results.
/stop Stops a server.
/summon Summons an entity.
/tellraw Displays a JSON message to players.
/testfor Counts entities matching specified conditions.
/testforblock Tests whether a block is in a location.
/testforblocks Tests whether the blocks in two regions match.
/time Changes or queries the world's game time.
/title Manages screen titles.
/toggledownfall Toggles the weather.
/tp Teleports entities.
/weather Sets the weather.
/whitelist Manages server whitelist.
/worldborder Manages the world border.
/xp Adds or removes player experience.