I noticed that I have a dearth of ramen information here, so I thought I'd update everyone with my current favorite places. Keep in mind that I adore とんこつ (tonkotsu: pork bone) soup, so I have a distinct bias for certain types of ramen. Still, I am slowly learning to branch out, so it won't all be about tonkotsu. Just most of it.
Also, I like tender, tasty pork (who doesn't?), and soft but chewy noodles. Al dente pasta I can understand, but not ramen noodles.
肥後のれん（ひごのれん）のひごラーメン：Higo Noren apparently has several shops but I've only visited the main branch in Shinjuku. The パーコーめん is the specialty, but I tried the Higo ramen on my only visit. All-around perfect とんこつ ramen! The pork was flavorful and tender, the noodles were the perfect texture, and the soup was delicious. The only down side is that the shop is small and a bit dingy. Not a place to go for atmosphere, but great for a bowl of ramen. I can't wait to go back.
天下一品（てんかいっぴん）のこってりラーメン：Tenka Ippin is a Kyoto chain which has a couple locations in Shinjuku alone. It's been reliably good, and wow, the thick soup is very densely flavored (this is not a healthy soup!). I like that, but people new to ramen might want to try the あっさり(assari) version, which is supposed to be light. I've only been there twice and I've gotten こってり(kotteri) both times. The noodles are the perfect consistency; soft but chewy. The pork is average from what I remember, and there is only one slice if you order the regular.
I shouldn't write these reviews when I'm hungry.