Can I just copy and past the Oblivion folder along with the folder my save files are in to another computer?

You can, but it's not wise to do it that way. First ensure you have the latest official patch installed on the present PC. Then install from the DVD onto the other PC, and again ensure the latest official patch is installed. Now copy the Data folder from the old PC to the new PC, and also copy the save files across too - do not copy Oblivion.ini, as some of the settings are specific to the old PC.

Doing it this way ensures that the Windows registry gets updated on the new PC, which some programs like Wrye Bash, OBMM, TES4Edit rely on to know where the game is installed to.

You also have to copy the related appdata sections or your modlist won't load.

If you have the Steam version of Oblivion, you can simply cut and paste the Steam folder to the new PC. After that, open the Steam client at least once and the registry entries will get created on the new PC. Then move the other files Vorians and Poketama mentioned.

Could you expand on that please?

Your selection of mods are in that directory. And there is one per user account. If you don't copy that, you just need to reselect the mods.

I just moved to a new computer. I figured the safest way is to simply re-install Oblivion, the DLC/Expansions/Patch, and all the mods. It was not easy, but I figure that is the safest.

Two methods I've used (this is from memory)...

If you're ok messing around with in the windows registry... Export the Bethesda\Oblivion hive from the HK Local Machine, import it on the new machine. You can check in the current user but I don't remember there being stuff there.

If you're not ok with the registry... Install OB from the DVD to where ever you want.

Then

Copy your Oblivion install to new PC. If you copied the registry from your old PC you need to keep the same install path as old machine, i.e. old PC installed to D:\Games\Oblivion copy to D:\Games\Oblivion on new PC. If you installed from the DVD this doesn't matter, just copy it over the install you just performed.
Copy your My Docs\My Games\Oblivion folder from old PC to same place on new PC. This has the ini, save games, etc in it.
Copy the c:\Documents and Settings\userID\application data\Oblivion folder to same place on new PC, this has your load order as mentioned above. You don't need this if you know what your load order is and can set it up again.

If you're going from XP to Win7 it's a bit more fiddly with the app data folder, I think there's an extra folder level in there, its c:\users\userID\app data\local I think it is.

I think that's it. As I said I'm writing this from memory. I did it twice in about 3 months earlier this year so that's why it's relatively fresh.


Hope it helps
:)