I am running Kubuntu Dapper-Drake on a Dell Latitude C610, 1 ghz cpu and 128 megs of ram. I have yet to be able to run a live cd/install with this little ram (except for DSL).
Were you trying to run a live cd version of Ubuntu before installing it? If you intend to go ahead with a download, you might want to try a direct install version instead. Here is a link for Ubuntu's Dapper Drake: http://releases.ubuntu.com/6.06/
Scroll down to "Alternate install CD" and choose the one for your system. Keep in mind that this is a direct install - you will get text based menus during the install, but no other interface.
If you want to just test drive linux, without installing anything at all, you could try DSL (Damn Small Linux), which uses very little resources and runs on just about anything, from what its website says. I did look at this, but only briefly, so I can't offer much there... You can get the iso here: http://www.damnsmalllinux.org/
Hope that helps!