While the meat and potatoes of my listening are singer-songwriters and rock, I do enjoy quality rap and hip-hop. I'm on the younger side of this crowd (although in my 30s, so not exactly young in the world of pop culture) and being a geek I enjoyed my cassettes of Young MC (1989?).

Because of the aforementioned dilution of quality as hip-hop became mainstream, it's a bit discouraging to sift through the current ranks in search for skills and quality. Some of the older classics have already been mentioned, but I'll add a couple.
Eric B and Rakim were a classic duo in the late 80s and Rakim did some solo work later. I like Rakim's "The 18th Letter", particularly the title track and "Guess Who's Back".
KRS One is another classic from the early 90s with a lot of skills. There's a single album "Retrospective" of his work.
These classics might not be the most accessible, but may be more so than some of the gangster rap days. That said, Snoop Dogg got famous because he is extremely skilled at rhyming and flowing - a skill that people lost sight of as his career progressed and then went in odd directions. I also enjoy a lot of Ice Cube's work.
While their newer albums became pop stuff, The Black Eyed Peas - "Behind the Front" did some jazz-infused work more like the mentioned US3 - Cantaloop.
Atmosphere was mentioned in this thread, so it's worth noting that they put out a free album online. The lyrical content isn't for moms and kids, but it's well done IMO. I like the use of horns.
http://www.rhymesayers.com/atmosphere/