Great topic!
I'm sure I can come up with more if I think long and hard about this, but one that comes to mind would be Smash Mouth's cover of ? and the Mysterians' "Can't Get Enough of You Baby." That one would irritate me to no end. Luckily, I haven't heard that cover in years! That band was also responsible for butchering The Monkees' "I'm a Believer." Ugh...
Others off the top of my head:
Not garage related, but Duran Duran covered Public Enemy's "911 Is a Joke," too. Unforgivable.
Motley Crue doing "Anarchy in the UK"
Michael Bolton's complete awful cover of Otis Redding's "Dock of the Bay"
Limp Bizkit murdering the Who's "Behind Blue Eyes"
And I'll leave it at this: