Question: I want to try Ubuntu on a desktop I just got, `DEll Optiplex 755`. It is a bit old, I think 2007. Will the new version of Ubuntu work on it? I am most worried about RAM and hard-drive space, and whether the graphics will work.

Answer: 
Refurbished Optiplex GX755

I did it for Ubuntu 13.04 and it worked really nice 
RAM upgraded to 2Gb,then 4Gb as a test
Video upgraded by using an AGP video card 256Mb,3D (Unity,Cube3D works fine)
HD 1 Tb

Now I'm about to upgrade Ubuntu to Saucy Salamander (13.10), without expecting a "downgrade" of the performances.

Ubuntu yours
It will work, but Unity probably won't run so well on it. Unity is the GUI that is standard in Ubuntu. Try installing Ubuntu with Gnome2 instead. There is an Ubuntu distribution that comes preloaded with Gnome desktop instead of Unity. 

<http://ubuntugnome.org/>

This is their homepage. You can download the latest 13.04 from there, or the beta 13.10. I would stick with the 13.04 since you are new, and having an OS that is in beta is probably not a good idea. 

If you're REALLY worried, you can try the even lighter version of Ubuntu, designed for legacy (old) hardware. Lubuntu. It can be found at their homepage here:

<http://www.lubuntu.net/>

It also uses the Gnome desktop, but installs light packages, and is overall less bloated than standard Ubuntu distributions. Perhaps you should try this first. 

Write a comment to this with the name of your processor and how much ram you have, I will make a suggestion.