rtcvb32: Same problem with Skyrim saves.
Why are they so big?
In the case of Skyrim I think it's because Bethesda saves every (or almost every) placeable item that is present somewhere in the world. You left a piece of armore there, a belt here, both get saved.
(hopefully I don't confuse it with another RPG right now)
Far Cry? Don't know. All it needs are flags for the opened chests, the inventory and stash. It's a much simpler game. You can't change the surroundings significantly and permanently.
Blackdrazon: You'd also want to use an Uninstaller if you want to delete save games and preference files in the process. Sometimes, the saves are put in the game's own folder, but they're often in your documents folder, the Windows AppData folder, and things like that. Worse I've seen a small handful of programs save in multiple locations for different purposes. Spares you the trouble of tracking them down.
Luckily save files are usually tiny so there's no harm in keeping them.
Savegames in the game directory are a no go these days.
If you install into c:\ProgramFiles or another directory where admin rights are needed, then the game would have to run as admin in order to be able to save. Therefore a directory in the userprofile is standard.
Windows offers some "My saved games" directory, but hardly anyone uses it.
My documents directory is so full of savegames that I created a subdir for actual documents.
AppData\Roaming gets synchronized between different PCs if you have a network user
AppData\LocalLow is meant for programs that need special permissions, games should not use it.
AppData\Local\<company>\<productName> would be the ideal place to save.
It becomes annoying if games like The Witcher or The Sims install mods and DLCs into the userprofile to avoid needing admin rights for installing downloads (even if that would be the correct way: only the admin installs software). Discord even puts the executable in the appdata directory