The Beach Boys are fun, flaky music, but they are genuinely gifted musicians and songwriters too. I figured out a while back that most people that joke them have never really tried to give them a chance.
The artists that immediately came to mind when I saw the thread title were Fleetwood Mac, Procol Harum and Meatloaf.
1. Fleetwood Mac has obviously been plenty successful just like the Beach Boys, but they never seem to get the respect they should. Musically, they are up there in the top 10 for pure musical talent. Lindsey Buckingham is one of those guitarists a lot of people leave off of their greatest guitarists of all time lists, but I put him right up there with Jimi in his abilities to do what most others can't. Their songs were good even before Stevie Nicks, but she brought a phenomenal voice and absolutely epic songwriting ability to the table. Fleetwood Mac is one of those bands a lot of people either don't admit to liking, or "forget" they like them, and they're much better than that.
2. Procol Harum probably get overlooked a lot just because they're British, but they are not only very musically gifted, but their music has the best timing of any band I've ever listened to. They know exactly the perfect time to hit each note, and when to let it linger. In my opinion, A Whiter Shade Of Pale is one of the greatest songs ever written. If you can listen to that song and hate it, you have no soul.
3. Meatloaf is fat and crazy. Or at least he was. His image is probably 100% responsible for holding him back and having nobody take him seriously, but the man is a musical and lyrical genius. I always loved when guys like him and Freddie Mercury brought theatrics into rock, because it always took it to another level to see someone so passionate and over the top.