Bman, I have a mid/low range PC the specs of:
1GB RAM
ATI FX 9600XT
AC97 onboard sound
P3.2 Ghz
And it runs fine for the most part, although it can be a bit laggy when lots of things are on the screen at once. Its usually as smooth as marble in dungeons though. But, and this is a big but, you can really customise this game in terms of the graphical settings such as draw distance and buffer sizes in the ini file that should be in C:\Documents and Settings\yourprofile\My Games\Oblivion\Oblivion.ini so it should run on most systems.
Personally its worth tweaking the grass draw distance so its lower than the default anyway, as at the moment things can die and disappear into the grass in the wilderness which is daft IMO.
The thing I love the most about this game is that your character really is customisable to how you want to play, like I've gone the heavy sword wielder / magic caster (spellsword) route but its equally possible to play a good thief with critical hits, a shadowy magic user, a ninja, a Paladin etc. If you unhappy with your start skills you can always make your own class which is another plus.
Its one of the latest games that has more content over style, althought the style itself is full.
Oh, if you want an example of the games humour play the first fighters guild mission and comapre it when you've finished to the Morrowind first fighters guild mission. A slight joke on the RPG Genre as well as an injoke at itself.