I have been playing Anachronox in Wine. Loved it (till I hit a game breaking bug). Thought I would share my experiences with others so they know what to expect - not sure if this is limited to wine.

The game was going great for the first half or so - no crashes at all.

Then, after I escaped the hero ship and discovered that pressing "\" sped up cut scenes, the game started crashing. I encountered the following bugs:

1. When I finished speaking to people, the game would not go back to the normal walking around mode, I had to press escape and then get back into the game to be able to walk around again. Same problem if I picked up objects.
2. i couldn't sleep. The game just faded to white and stayed white.
3. I couldn't use world skills. If I tried, the game just got stuck in world skill mode, I couldn't open doors or interact with objects.
4. I couldn't pick up the red crystal.
5. Most importantly, I couldn't get into the fortress in one gate. When I selected my team, I often had two boots' selected in one team and the game would always crash immediately after selecting the team.

So I don't know if there is limited to wine, or if a save game was corrupted or what, but just a warning for people that the game may not be perfect (if you haven't noticed already from the other comments).