I already posted in this thread (so don't take this as votes agreeing with previous posts, we may ne the same person), but here's a gimmick list of good and/or popular anime:
>Outlaw Star
I didn't really like it, but it's popular
>Record of Lodoss War
Many prefer the OVA, but I liked the TV version more
>Magical Stage Fancy Lala
I didn't like it, nor is it popular, but one can tell that it's objectively good. If it fits your taste, you'll like it.
>Cardcaptor Sakura
A very popular, and very good, classic.
>Cowboy Bebop
I've only seen a few episodes, and don't like it, but it's extremely popular, even with people with objectively good tastes, so you'll probably like it.
>Trigun
Popular. Haven't seen it, but popular enough that I can probably safely recommend it
>Princess Nine
Way underwatched, and very good.
>Yokohama Kaidashi Kikou
A classic
>Serial Experiments Lain
A must watch for any anime fan, a classic and a true masterpiece.
>Getter Robo Armageddon
I haven't seen it, nor is it popular, but I'm gonna bet it's good. It has one of the best opening themes in anime, full of energy.
>Kare Kano
Not enough people watch this. It's brilliant, amazing.