I love hearing well-known bands cover well-known tunes, as long as they keep it interesting and "make it their own," to use a tired old phrase. I think Aerosmith is a pretty good band, but their cover of Come Together didn't do anything for me. It's not bad, but it's also not very interesting to me.
Then there are the covers that aren't necessarily better than the original, but are different/interesting enough that they're still worth hearing - see most of the Across The Universe soundtrack.
I can think of two covers that improved on the original so much that they became the new 'definitive' versions: Jeff Buckley's Hallelujah (Leonard Cohen admitted this) and Hendrix's Watchtower.
In my mind, covers are great for live shows, when the band and the crowd are feeding off of each other's energy and everyone is just happy to be out having a good time. (Nickel Creek's live cover of Toxic by Britney Spears is pure unadulterated win). But if they're going to commit a studio album track to a cover, it had better be interesting.
PS - This isn't relevant to anyone outside of upstate South Carolina, but one of my singer-songwriter friends here does an amazing live acoustic cover of Huey Lewis' Power of Love. One of the best covers I've ever heard.