I've just recently installed Xubuntu 12.04 on my 10 year laptop and on my Acer Aspire One netbook and I'm wondering if the software that I run in Ubuntu 12.04 will also work in Xubuntu. I would think that it would work because they're very similar but I want to be sure about this.
No, not all software that works on Ubuntu 12.04 will work on Xubuntu 12.04.
You have to understand the differences between Ubuntu and Xubuntu are mainly the desktop environments: that means that most programs run just fine, except they are specific to the desktop environment and the corresponding programs (these are e.g. a different filemanager (nautilus | thunar), different window managers (unity-compiz | xfwm4) and so on).
So: if the software you are talking about needs specifically the window-manager or filemanager etc. then this software will not run without problems on Xubuntu. You will definitely be able to run those programs on Xubuntu, but that might come with problems (like filemanager switching, which might replace the icons on the desktop etc.).
The answers by the other authors probably relate to general programs like libreoffice, firefox, etc, which are not relying on specific desktop environments.
Yes all the software that work on Ubuntu 12.04 will definitely work on Xubuntu 12.04, after all both these Operating Systems are based on same Debian and Ubuntu base.
I think the bigger question is what software you are you wanting to install? IF it's a very heavy resource app, there might be an issue with speed.