I like anime too. I have a fair sized collection of DVD, Videos and Manga.
I like it as it's different. The stories are different. Humor is different. Some of the shows are just there to make you think.
Anime is not there for every one. Like my parents have a hard time trying to understand it.
And anime is not just the same. Both my flatemate and myself have totally different tastes in what shows we like to watch.
Anime has inspired a lot of movies today. Eg. The Matrix Trilogy.
Anime has also brought around more not-for-kids animations into the mainstream market. Eg. Enter The Matrix,
Dark Fury, Sin.
In the end, it up to you to make heads or tails of it. Like if i was going to recommend anything so a first time watcher, i would say :-
* Princess Monenoke
* Patlabor 2
* Ghost In The Shell
* Silent Mobius 1 & 2