So I decided to install Deus Ex, because even though I've played it, I've never gotten that far in it before. I had a bit of a problem getting it to run with the DirectX9, but I finally got it running. However, I have a couple problems. First, the speech gets sorta cut off near the end of the lines. I assume it's not supposed to be that way, but last night I thought I managed to fix it, only to discover this morning that it was back. Second, the mouse doesn't seem to move right. In the menus it seems too slow, and in game it seems kinda jerky. Which is a problem, since it's gotten me killed a few times already while playing. Can anybody help? Should I go back and use the DirectX that came with the game?

You might want to check Deus Exe out: http://kentie.net/article/dxguide/#downloads
Reportedly it helps with a lot of problems.
Also, I assume you snagged a Direct9 renderer from here, right? http://www.cwdohnal.com/utglr/
Try getting the OpenGL renderer from there as well and using that, it worked the best for me.
Last but very much not least, make sure the game's updated with the 112fm patch (do note the "m" at the end).

It's a problem with some mice and the Unreal engine. Also happens with the Quake engine. I have no idea why. I have that problem with Unreal and Quake with my latest mouse; haven't tried Deus Ex with it, but chances are I'll get the same problem too.

I haven't really figured out the solution to this problem, or even pinpointed the exact problem, but I hope that this at least gives you some hope that, nauseating as this may sound, you're not alone.

I have no idea how to disable mouse acceleration. I didn't use compatability mode, and I'm running on XP, and even then my Graphics card only runs DX9, which also seems to hate OpenGL. Don't know why. I did figure out at least how to deal with the mouse though. Apparently there was some VSynch thing that wasn't off, turning that off and setting a frame limit to 45 runs at a good speed and there doesn't seem to be the mouse issue anymore. I'm not certain if the speech thing is fixed since it seems random about when it actually works and when it doesn't. Thank you for your help, though. I appreciate it a lot..

Depending on your mouse and the drivers you have installed for it you might find the option to disable acceleration via the control panel.

Awesome. Thank you for your help.

You're welcome. It should be useful for future reference if not this time around. Sometimes mouse settings can cause problems with older games. Newer ones too. Especially with all the lazy console ports we get.