If you read Japanese, the Ramen DB is a great resource, as a repository of most of the Tokyo ramen fanatics' reviews.
So, I'll just introduce my personal favorites:
Interestingly, I've never tried their sister chain 野朗ラーメン Yaro Ramen although the tonkotsu smells pretty good. 156 Ichikoro has a slightly fancier ambience and is easier for me to enter.
2) Not ramen, but I'm going to stick it on this list because when I'm craving noodles this fits the bill just as well as tonkotsu ramen. 笹塚 Sasazuka station is a bit out of the way but it is home to 豪快 Gokai (map), the best 坦々麺 tantan noodles I've ever had. If you haven't had Japanese tantanmen, it's a creamy Japanese variation on the Chinese original. Cheap all the time, and pretty fast. Counter space only (12 seats). Just order the tantanmen 坦々麺 with the 細麺 thin noodles. They also do handmade thick noodles, but although I normally love handmade noodels, I don't like these as much as the thin noodles.
3) For tonkotsu ramen, I usually go to 博多一風堂 Ippudo. Easy to find around Tokyo. They have the thin, straight Hakata style noodles, and 2 regular types of tonkotsu - white is traditional, red is the revolutionary/modern version.
4) I like the salt ramen at 山頭火 Santouka (the fatty pork ぶたバラ is ridiculous, and can be a bit too fatty)
5) A chain restaurant found everywhere in Japan, 天下一品 has a こってりラーメン that is ridiculously thick. Apparently it's a chicken and vegetable based broth, but this stuff will probably leave you full for a day - it's that thick. I would recommend not drinking all the broth if you want to be able to move afterwards.
I hear the tonkotsu ramen at 一蘭 Ichiran is good, with the thin, straight 博多 Hakata style noodles. Next trip!