For all the people that do not like filler, do not read or watch InuYasha.  The main reason why that series lasted so long was because Takahashi just refused to kill Naraku.  When ever the series seemed to be starting to end, Naraku just came back through sheer will or something.  

Bleach - on going

Naruto - on going

One Piece - going

High School of the Dead - on going (Bra^ins)

Gundam 00 - 2 seasons complete (But I think there is going to be a 3rd season)

Gundam Seed - 2 seasons complete

Soul Eater - complete

Code Geas - 2 seasons

Want me to go on?

I would say no for HOTD only because it seems he's newish to anime and the fan service might turn him off. But on that note I wasnt expecting much coming into the first episode today and came out blown away..

Death note is the best anime IMHO, but I think it is completly different from Naruto.

Quick list off the top of my head

Durarara!

Noir

Wolf's Rain

Gundam 00

Burst Angel

DBZ Movies

Evangelion

Sword of the Stranger (movie)

Deathnote

Cowboy Bebop

K-On

Bleach

Naruto (skip the last like 25 filler episodes) and Naruto Shippuden

If you're looking to watch any of the really popular ones these guides are quite comprehensive:

Link 1 - This one is updated regularly.

Link 2 - Not updated as often (anymore?) but is more informative. It mentions episodes that may be only half filler, etc.

you weren't expecting much?  I knew it was going to be awesome from the trailer.  I'm surprised how much I enjoyed Mitsudomoe, thought it would be all cutesy but it was actually pretty funny. 

most of the series I would mention are already here but someone else did a movie so I'll mention Nausicaa and the Valley of the Wind.

Vision of Escaflowne and The Last Exile

Bubblegum Crisis original 80's OVA series

Bubblegum Crisis Tokyo 2040

Ghost in the Shell and Ghost in the Shell 2 movies 

Ghost in the Shell Stand Alone Complex and Stand Alone Complex 2nd GIG

these are some must see Anime as well.

Vision of Escaflone is awesome the musicle score by Yoko Kanno is some of the best music in Anime the Vision of Escaflone  is on pair with Evangelion for production values to.

Last Exile is awesome to.