Yeah, I recommend these. With extra weight put on my recommendation for Clannad because it hurts so good.ZehMadScientist said:Threads like these usually make want to post entire lists, but I'm going to refrain from doing so.
Steins;Gate - This is the series I always recommend, it's my favorite show. A Sci-fi thriller about time travel, with likable characters and a commendable plot. Tolerance for quirkiness is required, however.
Bakemonogatari/Nisemonogatari Haven't watched these
Clannad/Clannad ~After Story~ - Romance which will rip your heart apart. If you haven't seen it yet, I highly recommend doing so. (I guess this description isn't too motivating, is it >.>) Tears have been shed during this one.
It will possibly change how you react to sad stories forever.
Ah, I just remembered: Tengen toppa Gurren lagann fits your criteria absolutely perfectly.
Watch it!
Now please.
I'm positive you will love it.
Let's see... Large adventure, relationship, good animation...
Claymore may work.
FLCL is awesome and only 7 episodes long.
Katanagatari fits the bill very nicely.
Samurai Champloo: While I personally didn't like it that much, it fits your criteria well.