Beck - I haven't heard the two non-Mellow Gold albums he put out in 1994 and I also never heard Midnite Vultures or Morning Phase and those are all probably musts.
Sufjan - I adore Illinois and built a listening ritual around it that I do every year, and it was a slow build up, but that clearly is not going to happen again with Michigan, which has too many songs that were basically done better when they were given "sequels" on Illinois. As for the rest of his shit...uh, well, I really don't know anything about it. He's one of those guys where I really only bothered with one album that I adored, then heard a second that I was lukewarm on, and then forgot to do the rest of the 'scography because of it!
Beatles/Beach Boys - Well I know the hits, which will probably prove to be good enough for me. I'll never forget listening to 20/20 and thinking it was a really good album, but that I was also painfully overfamiliar with the five best songs because they were on hits comps!