My favourite melodic death metal is, with no doubt, one and only true forefathers of melodic death metal - Edge of Sanity. Those guys were brilliant, and offcourse, specially Dan Swano. Their combination of brutality, melody, mixture of death metal and prog rock (on later albums) is remarkable. They could have been the first death metal stars, winning wider audience, but unfortunately, they split too early. "Moontower", released in 1998 as Dan Swano's solo album, showed what direction they could take.

Regarding other bands, I like Carcass "Heartwork", In Flames "The Jester Race", some Dark Tranquility stuff, some Hypocrisy ("Destroyed" and "Edge of Madness" are great songs, good example to introduce someone with melodic DM), Amon Amarth are good...
Sometimes I like to listen Eucharist, Ceremonial Oath, Twin Obscenity... and yes, Dethklok is funny.

Though not exactly melodic death metal, but death/black mixture - there are also two excellent bands I like: Dissection and Unanimated. I can't separate their music and atmosphere from autumn rain or cold winter winds.
Also, Necrophobic, Vinterland, Sacramentum, Dawn and Mörk Gryning had some good moments, though some of them occasionally went on black metal field...

Discussing about melodic death metal and not mentioning At the Gates is not possible. So, here I go: I don't like them, I never did. I like only "Gardens of Grief". I tried and tried, wondering why they are so popular, but nothing, I don't get it.
Also, Arch Enemy - not my cup of tea. Though music is good, I never liked their vocalists, both Johan and Angela.