I'll start this with some of the more obvious stuff, and move onto more obscure bands later.
Sentenced: Finnish melodic death metal band of the early 90's with Taneli Jarva on vocals. Jarva left the band, and it slowly
started losing its metal aspects, and by now they're a goth rock band. Just released new album, "The Cold White Light"
Reccomended song: Desert by Night
...And Oceans: Finnish melodic black metal band that started in the mid-90's with a style akin to early Dimmu Borgir, but with much more originality and style than most bands of the style. ...And Oceans have a reputation as a bizarre band, with track names such as "Trollfan", "I wish I was Pregnant", "Odious and Devious" etc. Their third album, AM GOD, released a few years ago, saw the band moving away from melodic black metal, and into a fusion of black metal and techno/electro.
Reccomended song: Tears Have No Name
Thy Serpent: A one-man black metal project, the music of Thy Serpent is best described as atmospheric black metal. Using slow progression and intricate keyboard layers, Thy Serpent attempts to be dark, atmospheric and epic. Thy Serpent pulls this off suprisingly well, and keyboard use is very tasteful.
Reccomended track: Flowers of Witchery Abloom
Ajattara: Black metal side project of Pasi Koskinen from Amorphis, Ajattara is very grim finnish black metal. The pace is slow, and the music is heavy and crushing, with clear doom influences. Playing is very clean and professional throughout, and keyboards are used as a supportive instrument, never taking the main role.
Reccomended song: Yhdeksäs
Impaled Nazarene: Finnish players of hyper-fast black/death metal, Impaled are self-proclaimed players of nuclear metal. Surely one of the most punk metal acts in Finland, the band occasionally resembles hardcore punk more than underground metal. Though their original goal of playing music as loud and fast as possible has given away to more melodic aspirations, although they still can't be called soft.
Reccomended song: Total War, Winter War