Mods for pre existing games?

[Blind]

Is it possible to make mods for games that run on this engine like Far Cry 3 or Crysis?

[Southpaw]

Neither of those games run on CRYENGINE.
If you want to make mods for Crysis, use the CryEngine 2 Sandbox Editor.

[Adsolution]

Indeed. For note, Far Cry 2/3 run on a modified CryEngine1 which was sold to Ubisoft, and they renamed it the Dunia Engine. Like maddog said, Crysis runs on CryEngine2, the previous CryEngine.

- You aren't allowed to mod other games with this engine service, only create your own.

[theystillspyillegally]

There are free tools out there for modding Far Cry 3 and Crysis as stated above. Most games now-adays that are big sellers (and even some that aren't) include tools (or have tools readily found by those who know where to look) to make modifications to the base-game and otherwise facilitate creation of user-added levels/items/weapons/characters and such. Since the days of DOOM, user-content creation has exploded, and it's only fitting that pc gamers get thier modding fix in.
If you want to make your own game, you are in the right place though as this engine looks really top-notch and makes (what I am working with) Unreal Engine 2 look like...Doom.