Anime Tv Shows.

I have a lot of favorites, but I'll follow OP's example and pick 5.

Sword Art Online(only found it the other day, but I love it)

Code Geass

Full metal Alchemist

Naruto Shippuden, though the original is almost as good if you skip the filler

Busou Renkin

I'm also a fan of several comedies and harems, but none make my top 5.

Following the tradition of 5 I would say:

Paranoia Agent

Haibane Renmei

Kara no Kyoukai

Fate Zero

Ghost in the Shell S.A.C.

1:Case closed
2:Shakugan no Shana
3:Lupin III
4:Kateikyoshi Hitman Reborn
5:To Aru Kagaku no Railgun

i have other favourite animes but they are well known to many
so these ar my top 5 for now

Keeping with the top 5 and tryin not to do copies...

1.Gurren Lagann
2. Murder Princess (only like 6 shows, so kinda like a movie split into episodes.
3. Aquarion
4. Soul Eater
5. DBZ (Grew up with it)

I probably got top 3 that I actually love
1. Last Airbender (grew up with this show, will always think its one of the best shows ever).
2. Highschool of the Dead
3. InuYasha

Alright my turn and I'm being a completely hipster and going with top 10 because yeah I'm going to roll like that.

1. DeathNote
2. Rurouni Kenshin
3. Queen's Blade (only suggest watching this one if you're 18+ if you're not don't watch it.)
4. Blood+
5. Samurai 7
6. Eureka 7
7. Murder Princess (Yea I'm requesting the same as agentyamski but this is a really good anime.)
8. Deadman Wonderland
9. Mortal Kombat (before you say anything yes this is an anime as well as a video game and it was pretty badass)
10. Aquarion (yes another suggested by agentyamski but again it's really good and we do have a lot of the same taste in anime.)

My favorite anime shows have to be:
1. Chobits
2. Yu-Yu Hakusho
3. Ah! My Goddess
4. Rosario+Vampire
5. Any Key Work( Clannad, Kanon, Angel Beats, Air and Little Busters)
6. Toradora
7. Familiar of Zero
8. Zatch Bell
9. Nadia Secret of Blue Water
10. Highschool DxD

One Piece
Black Butler
Hetalia
FMA:Brotherhood
Ouran High School Host Club (I forgot is high school was one word or not x.x )

Steins;Gate
Naruto
Fullmetal Alchemist
Log Horizon
Kill la Kill
Toradora
Dragonabll Z
Ouran High School host Club
Tiger & Bunny
Sonic the Hedgehog (OVA)
FLCL
Ergo Proxy
Cowboy Bebop
Fullmetal Alchemist Brotherhood
Tengen Toppa Gurren Lagann
Clannad
CLannad: After Story
Gargantia on the Venturous Planet
RWBY (Anime Inspired)

I haven't watched much anime recently, but:

1. Shingeki No Kyujin
2. Durarara!!!
3. Yugioh series (up to 5d's)
4. Bleach
5. Soul Eater