Linux/GNU - Ubuntu 10.04
CrossOver Games 9.2.1
Nvidia GeForce 8600 GT
I had problems trying to get Steam to launch the game. After pressing the 'Play' button in the game library, there was no RA3 splash screen. However, after I kept pressing the play button several times and confirming it to launch the game, I'll get a splash screen and the game runs fine.
In-game, everything works - no crashes or corrupt images etc.
EDIT
Updated CX Games to version 10 and it resolved the Steam launch issue.