Clannad: Dont watch the anime, read the VN instead, seriously.
Berserk: Pretty awesome, also has a sequel in the making. Finally.
Cromartie High School: Great humor, what else is there to say?
Penguin Musume Heart: Why would you even want to watch this? It's garbage.
Sugar, A Little Snow Fairy: Nothing much to say here, cute, childish anime aimed at little girls and 30-year-old men.
UFO Ultramaiden Valkyrie: Not seen, doesn't look very promising though.
High School of the Dead: Ugh. No. Zombies + anime sounds like it could have potential, but you won't find it here.
To Aru Majutsu no Index: I hate Index, but it's got to be popular because of something, so try it, I guess.
Gurren Lagan: Brainless thrill ride, very enjoyable, not very sophisticated. (That means it's good)
K-On: It's alright, but I've seen better humor and better moe elsewhere.
Excel Saga: Decent humor, often hit and miss however.
Welcome to the NHK: Great, still one of my favorites, although the book and manga are slightly better than the anime.
Moon Phase: If I say I liked it I won't be able to face myself in the mirror. But I did. Not much to say about it, cute characters, silly story, fanservice, etc.
Sayonara Zetsubuo Sensei: Amazing art, great humor, goes "extreme" in second season, which you may or may not like.
His and Her Circumstances: Never seen.
Love Hina: Don't know, I liked it but it's so old now I highly doubt it's still very enjoyable. One of the first popular harem and it's been copied to death.
In conclusion: How should I know? You threw several genre on there, so watch what you want. If this is everything on your list, I'd say:
Action: Berserk, TTGL
Humor: Cromartie, Sayonara Zetsubo Sensei
Slice of life: Depends, either K-On or Sugar, whatever has more "appeal" to you.
Romance: His and Her circumstances (because you'll read Clannad)
Oh and add NHK somewhere on there, too.