Sure you can have just Linux installed on a Computer.
I thoroughly recommend Linux Mint 9 LTS which is built upon Ubuntu 10.04 LTS its easy to install and easy to use plus it comes with much of the software you are likely to need preinstalled
Linux Mint 9 LTS Download
http://www.linuxmint.com/edition.php?id=52
Linux Mint 9 LTS Installation Guide
http://www.linuxbsdos.com/2009/12/03/linux-mint-8-installation-guide/
Linux Mint 9 LTS Release Notes/User Guide
http://www.linuxmint.com/rel_isadora.php
You download the ISO. image of Linux Mint 9 LTS then you need to create a Bootable LiveCD for installation
https://help.ubuntu.com/community/BurningIsoHowto
Linux Mint 9 LTS can also be run direct from the LiveCD from Boot without touching your Hard Drive
Once you have installed Linux Mint 9 LTS you can bring it up to date with easy tweaks like upgrading the Kernel to 2.6.38 and installing Firefox 4
Upgrade to Kernel 2.6.38 on Ubuntu 10.04 LTS/Linux Mint 9 LTS
https://sites.google.com/site/lightrush/random-1/howtoinstalllinuxkernel2638onubuntu1004lucidfromubuntu1104nattytheeasyway
How to install Firefox 4 in Ubuntu 10.10 / 10.04 from the Firefox PPA (stable)
http://www.webupd8.org/2011/03/install-firefox-4-in-ubuntu-1004-1010.html
LUg.