On the package, it's just called "One For All Learning Universal Remote Control," but at the bottome of the manual it's got the number "URC 8810W". It's not the be-all, end-all of remotes, but it's worth the $20. Wal-Mart carries it, although Best Buy sells a remote that's nearly identical except for the inclusion of a small LCD window. Same brand but $50 instead.
They claim they have the deepest preprogrammed code index in the industry, and I can attest to the thoroughness (I haven't stumped it yet, even with some old, old stuff). If it doens't cut it in the main rig, just use is for something else.
I doubt it will run every function of every component (at least not without some teaching) but it sure covers the high points. It's not on the same level as the MX-500 (it doesn't have as many learning functions) but hard to beat for the price. Plus if you buy it at WallyWorld, you can certainly return it if you don't like it.