Embarrassment Cover Tunes

Pushin' Too Hard by the Seeds was the first Embarrassment cover song to make it to vinyl, on the BOMP compilation. Featured on the Pebbles compilation that influenced many punk and new wave bands, the lyrics matched the sentiments of several John Nichols' originals.
Don't Stop (Til You Get Enough) was a Michael Jackson song done with loving ardor in their own style. This was frequently mistaken for a joke, when in fact it was performed as a cover of a pretty decent, though unhep, song.
Time Has Come Today was a rather apocalyptic song about being down in the dumps done by the soul group the Chambers Brothers, and fit the recession-era mood precisely. A number of contemporary bands also covered it, including (later) the Ramones.
Immigrant Song by Led Zeppelin was occasionally performed and made it onto Heyday

Maybe Baby (Buddy Holly)
No Reply (Beatles)
Street Life (Roxy Music)
Rebel Rebel (David Bowie)
Drunkest Man in the World (by Jim Rosencutter, vocals by Ron Klaus)
Money (Berry Gordy, via the Beatles version)
Pretty Woman (Roy Orbison) A standard of the later live show.
On Broadway (George Benson) Also a standard, often used for an encore.
Funtime (Iggy and the Stooges) An awesome version of this closed many sets.
Burning Love (Elvis Presley version). This made it to the God Help Us studio and was featured in several of the reunion gigs.
Instant Karma (John Lennon) This also made it to some of the later reunion gigs.