Fruits Basket, of course, is a great read, definatly one that could help you get into manga.
Love Hina, also mentioned by Concrete Badger, has been used sucessfully to get people into manga by me four times; it's slapstick humour is particularly popular with young men, for obvious reasons.
Neon Genesis Evangelion, once again mentioned by Concrete badger, is a good adaption of the anime and well worth a read.
For a more action packed read, Hellsing is beautifully drawn, has a good plot and cast and features lots of action
Berserk, likewise, although it's more violent and set in a gritty medieval fantasy setting, while having a completely different style of story.
The Shounen Jump titles that I would personally recommend are Bleach, Hunter x Hunter and Kenshin, but of course Naruto is currently the most popular one. One Piece makes a fun light read, too.
Beck, the first volume only out, is another great introduction to manga.
Death Note likewise, the first volume either out now or coming out soon.
There's many many titles worth a read; just go to your nearest bookshop where manga is sold, and find one with an interesting storyline, and then take it from there!