To get the game running and to avoid most issues, install vcrun2005 from winetricks:
Better sound issue fix reported by Adys:
Crash on login:
Disable Steam Overlay Renderer (rm GameOverlay* in steam folder after opening steam, but before opening Worms)
ATI ISSUES (reported by Callum Fare)
Here's a guide on fixing any Radeon-driver related crashes with Worms Reloaded. This method will execute Worms with the r300g driver, instead of the default r300 driver. This method will (probably) not work for people with a HD2xxx or newer graphics card.
1) Download the r300g libraries: www.mediafire.com/?3mz6711gu36u08j
And extract the archive into your home folder (so you end up with /home/yourname/r300g/)
2) Make a new document on your desktop, or wherever. This will be your shortcut to open Worms. Call the document "LaunchWorms.sh"
3) Paste the script found here into the document: pastebin.com/raw.php?i=dgq9mmrk
4) If you're running 64-bit, then swap /32 with /64 in the driver path.
5) If Steam isn't installed in the default path, edit the wine command appropriately.
6) Save the script, then right click it, go to Properties > Permissions and tick 'Allow executing file as a program'.
7) Double click your shortcut and hit Run.
8) Enjoy playing Worms!
For best results, as always make sure Compiz is off, and use the 2 winetricks fixes also posted.