I have a lot of the same stuff you likely have, a mixture of top hits, "classic rock" (whatever that is anymore), other popular stuff, and some offbeat songs,. Rather then naming everything, I thought I'd list some of the lesser known stuff I listen to.
Here they are, with my impressions, in no particular order.
1. The Fabulous Poodles. This mostly forgotten group had only 1 hit in the U.S. ("Mirror Star", in the late 70's), but they were AWESOME. They did some of the most eclectic stuff ever, blending violins with modern rock instruments, and songs that span a remarkable gamut of styles and odd topics (suicide, dessert, anorexia, artificial body parts, vampires, etc.). A sampler collection called "His Masters Choice" is still out there on CD. It doesn't have all their good stuff on it, but it's still awesome.
2. Spinal Tap. Created for the excellent mid-80's movie of the same name, this group has endured, to the extent that some people now don't realize the whole thing started as a joke. Their collection of intentionally badly written lyrics and tasteless music somehow remains quite entertaining. I was listening to Spinal Tap long before I ever dreamed I'd be doing spinal taps for a living.
3. Shriekback. Okay, I only have 1 song by them ("Nemesis") but let's face it- how many other dance numbers feature the science word "parthenogenesis" in the chorus?
4. Sisters of Mercy. Again, I only have 1 song by them ("This Corrosion") but this dance number is remarkable for it's catchy beat, 10 minute length, and absolutely senseless collection of lyrics. The random phrases sound like something written by a guy with left-sided brain damage (which, for all I know, they were).
5. Tom Lehrer. American humor music is a triad of Tom Lehrer, Allan Sherman, and Weird Al Yankovic. All are good, but to me Lehrer is exceptional for his style of writing, and blending it with his advanced knowledge of mathematics and science. Allan Sherman is mostly forgotten today (he died in 1973), but his influence on all who've come since is unmistakable.
6. Maggie Estep. I may be the only person on Earth who bought her CD "No More Mr. Nice Girl", but it's awesome. More of a collection of poems read to music then true singing. But how can you NOT like a song featuring lyrics like "Fuck me and take out the garbage, feed the cat, and fuck me"? And her monologue "Bad Day at the Beauty Salon" is unforgettable.
7. Al Stewart. Remarkable stuff. Known primarily for his 1970's hit "Year of the Cat" and a few others, he remains an excellent songwriter and performer, who does fascinating work based on historical themes. His live album "Rhymes in Rooms" of just him and acoustic guitars, is one of my favorites. Ever.
8. Saturday Morning's Greatest Hits. What a great idea. Get a bunch of 1990's bands together, and have them re-record the theme songs from the 1970's cartoons I grew up listening to. Liz Phair's version of The Banana Splits" theme is awesome, and the album continues strong all the way through. Underdog. Hong-Kong Phooey. Speed Racer. Scooby Doo. Fat Albert. The Groovy Ghoulies, and many more. A related album of remade "Schoolhouse Rock" songs was okay, but not as good as the cartoon themes.
9. Gary Numan. Mostly remembered for his only U.S. hit "Cars", he actually had 3 interesting albums in the 1970's (Replicas, The Pleasure Principle, and Telekon) which were pioneering works in the use of synthesizers.
10. The Refreshments. Their album "Fizzy Fuzzy Big and Buzzy" is excellent. How many relationship songs have the chorus "I can't sleep, 'cause she snores like a chainsaw!"?
11. Northern Exposure. One of the few TV shows which I really, really enjoyed. The music CD contains an extended version of the theme song (which my mother calls "The Moose Dance") and a selection of songs played in the background during the show. They vary from Nat King Cole to Magazine 60 to Lynyrd Skynyrd.
On an unrelated note, I think this was one of the best TV series, ever. Did anyone else out there think it should have ended with the episode "The Quest", which featured Joel and Maggie looking for the "Jeweled City of the North"? To me, that one hit the right notes to end the show on, but instead they dragged it out for a few more episodes.
12. Sparks. Were these guys great, or what? Their greatest hits set contains their only popular song ("Cool Places"), a delightfully generic dance number called "Music That You Can Dance To", and even a song about sperm ("Tryouts for the Human Race").
13. The Dead Milkmen. These guys mastered the art of the quick song, with some of their stuff being less than a minute. The rambling musical monologue "Stewart" begins with the line "I like you, Stewart, you're not like the other people, here, at the trailer park" and goes on to discuss an accidental decapitation at an amusement park and paranoia about the government being in cahoots with homosexual martians to poison the soil.
14. Cast. These guys never really took off in the U.S., but I for one thought they were great. Their album "All Change" is a neat collection of songs that blends a 1960's retro sound with more modern stuff.
15. The Disneyland Soundtrack. Yeah, I know. I guess this is a hazard of going to the parks as a kid, and now having gone with my kids. It's simply a collection of music from the rides (yes, including the dreaded Small World) but is oddly entertaining. And certainly brings back memories. If you're driving when they hit the launching point in "California Screaming", it's hard to resist mashing the gas pedal and pretending you're on the ride.
Not an inclusive list, but for the inquiring minds who wanted to know, now you know.