I've actually seen Sesame Street listed in some articles by people complaining about certain kids' music that they find trite or annoying, and I'm always baffled by that. To me, Sesame Street is some of the coolest kids' music. I used to watch the show when I was little, and I don't remember it much from then, but I've now rediscovered its brilliance through watching the show with my two daughters.
Musically, the Sesame Street songs (mostly by Joe Raposo and Jeff Moss) are of a musical theatre nature, but in the very best sense of being hummable, humorous and mostly upbeat. If you watch the show day in and day out, there might be some blah songs here and there, but many of them are great, and if you watch or listen to a "best of" collection with Sesame Street songs it's a truly incredible list of memorable tunes; "C is for Cookie", "Sing" (made more famous by the Carpenters, but it was a Sesame Street original), "Rubber Duckie", "Doin' the Pigeon", "I Love Trash", "I Don't Want to Live on the Moon", "Monster in the Mirror", "Put Down the Duckie", "What's the Name of that Song", "I Dance Myself to Sleep", "It Ain't Easy Bein' Green" and of course the theme song itself. And yes, I even love "Elmo's Song", which is a very funny gimmick put into a very catchy song. There are also many clever "style parodies" and direct parodies on Sesame Street, including "Can You Count it Higher" and "Telly's Lunch". There are also many great musical moments on the show with guest stars like Andrea Bocelli, Paul Simon, James Taylor, B.B. King, etc.
So if you're somehow writing off Sesame Street as annoying kids' music, but haven't seen it in a while and think their musical output equals Elmo's daily "Jingle Bells" rephrasings (which are kind of annoying), I suggest you give it another chance. Watch the 25th anniversary special, which includes a lot of the above songs, or pick up the box set, which includes those songs and a lot more. Very cool stuff, indeed, and still one of the best things going in kids' music.
Sesame Street website