I am making a game using the Unity game engine. I want to save the player's progress including level, experience points, chosen character, etc. Presently I am using playerprefs but I want to know whether this will work for gamers who will run this game on their mobile devices (Android/iOS) as well as desktops (OSX/PCs)? If not, then how should I save this information? I want to auto-save player progress after clearing each stage.
PlayerPrefs will work cross-platform, but it's not recommended for gameplay progress save files because it's insecure. As a plaintext file, a player can easily open it up and change the contents to cheat, or make your game behave unpredictably. It's also not guaranteed to stay around.
PlayerPrefs is intended for non-essential preference information, like control mapping or music/sfx settings - things the player can freely change anyway, and wouldn't miss terribly if they were to (on Windows for example) use a system restore point and lose some of their registry information. If this lost their high scores or campaign progress, players would be justifiably upset!
Instead, it's recommended to save gameplay progress in your own file (usually binary, possibly encrypted or signed if you want to make it harder to modify, but see Philipp's comment below on this).
You can use Application.persistentDataPath to get a reliable save location on each platform. This is typically in a user data folder that won't be wiped out in cases like the example above.
Once you have a path to save to, you can use the regular C# IO methods to create, write, and read your file. The details will vary a lot depending on your save file format and structure, so if you run into trouble, it's best to ask a new question detailing what you're trying to do and where you're stuck.
On the Unity site, there is a video that goes over the two main options for saving (PlayerPrefs and creating your own save file). The video can be found here: http://unity3d.com/learn/tutorials/modules/beginner/live-training-archive/persistence-data-saving-loading?playlist=17117