Alright...let's see here. Bear in mind, you asked for greatest animes I'd seen, not my favorites. There's a difference.

Now, in no particular order:

Hellsing

This show was great. Perhaps the best rendition of vampires I have ever seen. Seras was a great character and gave us the rare opportunity to observe how a person copes with waking up as a vampire. I also love the idea of using SAS to hunt vampires. That my friends, is how it is done.

Who dares, wins.

Trigun

I loved this show. Three words: Vash the Stampede.

Vash is one of my all time favorite anime characters. I usually hate the goody-goody type (I'll get you superman!!! Just you wait!!!) but Vash was different. He's that way for a reason. And he has to struggle everyday to stay on his chosen path. The show can seem like it's just goofy and fun, but that's just a facade. Underneath that illusion you will find a show that is dead serious, and a story that is quite tragic. Just like Vash.

And Nicholas D. Wolfwood is my hero.

And for the life of me I can't think of a third.

So...how about...

Magical Shopping Arcade: Abenobashi?

That show was just so monumentally weird. Seriously, I never knew what to make of it. And since I can't think of anything else, why not?