I bought this game and I haven't been able to play it properly yet. The reason for that is that I can't walk without having to always jump first. Otherwise the character only turns to that direction. I saw a thread here on the forum of someone having the same problem but the "solutions" didn't really work good for me.
One solution was to download a program called CPUKiller which sort of helped the problem though causing a new problem, making the game really laggy. Also, you could only use it for 20 minutes before trial was over.
The other solutions in the thread didn't work at all so I'm wondering if anyone else is having these problems?

You are not talking about the gog-Version of Outcast? This version does not have the slowdown-bug, which depends on fast CPUs.

It's the gog-version. My character also moves in slow-motion when walking in the mud which is very frustrating

This is curious indeed. Normally there is no slowdown with gog-Version, at least here with WinXP. Had you installed another version of outcast and did not remove it before? Apart from that i only can advise you to uninstall and reinstall the game, maybe it helps ;-)

Did you read this?
http://www.gog.com/en/forum/outcast/walking_in_the_mud/?search=slowdown

This is my first time playing this game so I hadn't any other version installed when I bought this. I tried re-installing and re-downloading it, but it's still the same. I tried out the patch which was supposed to fix the bugs, but it only gave me a better screen resolution. I still walk in slow-motion through mud and can't move without having to hold some random key first.

OK, so the walking in the mud thing is actually the intended behavior, by the modder who made that fix. GOG incorporated his fix into the game to fix the processor speed problems... fast processors used to make it nearly impossible to move in the mud and also when riding a Twon-ha, it wouldn't move. The modder fixed that problem and made a conscious decision to have Cutter move at walking speed while in the mud.

I don't know why you have to hold the jump key before being able to move. That is very strange. Can we get some information on your system? What OS are you using? Did you install the game as administrator?

Also be sure to read the thread that Delgado linked to, the modder who made the fix has actually posted there explaining it.

I saw his post now, I must've not turned the search filter off properly the first time. Regarding my system and OS, I use Windows 7 64-bit, Intel i5, GTX 470, MSI P55A-G55. I've tried installing it both as administrator and by continuing with the autorun that starts when the game is downloaded.

I tried downloading patch4 from http://www.planet-adelpha.net/Downloads/patches.html to see if it would make a difference, but it didn't.

Also, it's just not the jump button, I've realised that any button that does something seem to work, as long as you hold/press it before you walk.

You are also running the game as admin, right?

Anyone else know why the controls would be wonky? There was another thread where people discovered weird behavior if their taskbar was moved to anywhere other than the bottom of the screen, so if you've got your taskbar set up on the sides or top you could try moving it to the bottom. But I think that was weird behavior with the launcher buttons, not the game itself.

Yes.

My taskbar is at the bottom of the screen also.