My personal top five list for both Anime and Manga:

Anime
Tengen Toppa Gurren Lagann; wiki, MAL [comedy, drama, mecha]
Kimi ni Todoke; wiki, MAL [romcom]
FLCL; wiki, MAL [scifi, surreal, comedy, mecha]
One Piece; wiki, MAL [action, comedy, drama]
Gintama; wiki, MAL [comedy, parody, scifi, action]

Manga
Honey and Clover; wiki, MAL [comedy, drama, romance, slice of life]
I''s; wiki, MAL [comedy, drama, romance]
Hot Gimmick; wiki, MAL [comedy, drama, romance]
Genshiken; wiki, MAL [comedy, slice of life]
Love Hina; wiki, MAL [comedy, harem, romance]

however, if I were to suggest something, then these would be my suggestions; with added information links from Wiki and MAL (since you can normally find links to subber's home pages from the MAL links).

If I were to suggest an anime to watch, I think my picks would be:
Baccano; wiki, MAL [adventure, comedy, fantasy]
Genshiken; wiki, MAL [comedy, slice of life]
Welcome to the NHK; wiki, MAL [dark comedy, drama, slice of life]
Detroit Metal City; wiki, MAL [comedy, music]
Minami-Ke; wiki, MAL [comedy, slice of life]
REC; wiki, MAL [drama, romcom]
Kimi ni Todoke; wiki, MAL [romcom]
Beck; wiki, MAL [music, romance, slice of life]
Rurouni Kenshin: Tsuiokuhen; wiki, MAL [drama]
Honey and Clover; wiki, MAL [comedy, drama, romance]
Paranoia Agent; wiki, MAL [mystery, horror, satire]
Ouran High School Host Club; wiki, MAL [drama, romcom]

Also, if you're looking for a Movie to watch:
Paprika; info, MAL [or another Satoshi Kon film [wiki, MAL]]
Steamboy; wiki, MAL
Voices of a Distant Star; wiki, MAL
Robot Carnival; wiki, MAL
Lupin III Castle of Cagliostro; wiki, MAL [or another Lupin 3rd film [wiki]]
Angel's Egg; wiki, MAL
Castle in the Sky; wiki, MAL [or another Studio Ghibli film [wiki, MAL]]