Okay, you've heard me squealing about this one, so i shall put this on the table:
If you've never heard of CLAMP (fat chance) they are a group of women who make manga, including Cardcaptor Sakura, Chobits, Magic Knight Rayearth etc. Tsubasa and it's brother XXXholic are the end to cardcaptor sakura, Tsubasa in particular is full of reference to the clamp universe. but don't judge it too quickly. They're both their own stories really.
Tsubasa is about Shaoran, a young archeologist in the land of clow. One day while in one of his exavations, his childhood friend princess sakura comes presumably to visit him when something happens that causes her to lose her memory. Shoran now must cross dimensions in order to recover it, while discovering dark secrets about his own past as well.
It sounds cheesy and i'm missing alot, but i love it, so don't question it
XXXHolic is about Watanuki Kimiro, a high schooler who can see evil spirits that plague his every moment. One day he is mysteriously led to yuuko's shop, a shop that grants wishes to those who need it. In return for getting rid of the spirits, Watanuki works part time in yuuko's wish shop, where strange things seem to be a daily thing.
Yet again i'm not putting it quite right, but it's worth a look, especially for big Clamp fans (If there should be any in RMRK .-.) And even if you're not a clampophile these are great series on their own.
Some key differences between the anime and manga:
I haven't seen much of tsubasa, i've read all of the manga however and so far they seem to be at least relatively close together in terms of storyline, but XXXholic is another matter: One of Tsubasa's + XXXholic's main story points is the fact that they meld with each other constantly (Due to ideas of crossing to different dimensions and wish-granting) but in the XXXHolic anime the tsubasa world is cut off completely. For this reason alone i recommend that you pick up the manga first because many of the manga plotlines will not make sense if you watch the anime first. Also they smoke more pot or whatever in the anime. Don't do drugs, kids.