I ran it fine on my old puter with Vista. I now run it fine on my new puter with 7.
I do run some mods and I follow this advice from the mods forum FAQ for Vista users:
For best results, it is recommended to install Oblivion to a location other than the default C:\Program Files\ folder. Another location such as C:\Oblivion\ or D:\games\Oblivion\ will work better. This will avoid the file permission problems many users have experienced due to the increased security restrictions Vista places on the Program Files folder.
I play it on Vista. I run it in the default location and the only problem I've experienced is not being able to open the console, but I think that's more my Keyboards fault, apostrophe's appear as colons.