I just tested some games on a GNU/Linux Live System (Knoppix 6.3 - Linux Kernel 2.6.32.6 - it's a 32-bit OS version) with Wine 1.0.1 default (pre-installed).
Besides a mouse-related issue (workaround: 'jump-when-you-want-to-turn-around-beyond-view-of-sight' - otherwise see winehq.com for solution) OUTCAST looks sharp and runs/controls fine!

Also post this in "GOG games that are working fine with linux wine" topic. Also mark it as your favourite (by ticking the 'This is my favourite topic' box at top of the topic) so you can always see if there's new posts in that topic.

I've been playing GOG.com's Outcast using Crossover on my mac. It's based on Wine so I got that same mouse problem you mentioned, but solved it by using a gamepad =)

@Petrell thanks for the hint.
(I did do a forum search, but only "outcast+linux") = fav'd the linux-thread now.
@tassitassi using a gamepad? that is brilliant!

Yep. It runs perfectly =) My only problem was reassigning the keys in Outcast, but solved it by mapping it in the OS, instead.
Have fun!

Yup, runs fine on my 64 Bit Ubuntu 10.10 with WIne 1.2.1. But I can't get it to run in fullscreen. Wine always shows a desktop and the outcast screen never scales but shows the small 640x480 area on my 1600x1200 LCD. No matter if I config wine to emulate virtual screen or not. Any idea?

UPDATE: with the Hi-Res Patch in the forum, now I get up to 1280x768! :-)