All of us probably know more than enough music in English. However, it might be difficult to get oriented in the music using your non-English target language which is the reason why this list was started.
As you probably know others (especially in your native languages), please share!
The list is sorted by language used in lyrics (even if it is used only for some songs), nationalities don't matter.
Please remember that the list is based on the taste and memory of its participants and therefore cannot represent the whole specter of music in various languages. It's up to you to find your path and taste, enjoy :-)
Belarusian
Камаедзіца folk rock/metal
Czech
Znouzecnost punk
Nightwork
Wohnout punk
Chinaski pop
Karel Gott old legend of popular music
Finnish
note: you can find a lot of great bands at MetalFromFinland.com, but many sing in English and some in Swedish (most notably, Finntroll)
Korpiklaani folk metal
Harmaja rock
Ruoska industrial metal (nicknamed "the Finnish Rammstein")
Viikate rock
Teräsbetoni power metal (were at Eurovision-2008)
Mokoma thrash metal
Nightwish symphonic metal (only a few songs in Finnish)
Uniklubi rock
Moonsorrow viking metal
Yö rock
Verjnuarmu doom metal ("Savo metal" sung in this dialect)
Tapio Rautavaara folk/traditional, classics
Ajattara dark metal
Kolmas nainen pop/rock
Lama punk
Auringon hauta folk metal
Tuomari Nurmio rock
Turmion kätilöt industrial metal
Jenni Vartiainen pop
Chisu pop
Apulanta pop/rock
Raptori hip hop
Fintelligens hip hop
Suvi Teräsniska pop
Jukka Poika reggae
Soul Captain Band reggae
Vesa-Matti Loiri classic pop&rock
Paula Koivuniemi pop
Olavi Virta tango
Kaija Koo pop
Ultra Bra "big band" pop
Popeda rock
Kirka pop
Eppu Normaali pop
Anssi Kela pop/rock
J. Karjalainen pop/rock
Movetron dance
Frederik pop
Antti Tuisku pop
French
Stromae hip hop, electronic, pop
Édith Piaf chanson, ballads
Zaz french pop,jazz, soul
Jacques Brel french popular music
Manu Chao punk, rock chanson, salsa,reggae, ska
InGrid dance music
Noir Désir rock
Kain Quebecois folk rock
Natasha St-Pierre Canadian pop singer of Acadian origin
Gaulish
Eluveitie folk metal
German
Falco Neue Deutsche Welle, pop, rock
Rammstein industrial metal
Lacrimosa gothic metal, rock
In Extremo medieval metal
Italian
Luciano Ligabue rock
Vasco Rossi rock
Caparezza hip hop
Carmen Consoli pop
Miodio pop (from San Marino)
Nek pop
Laura Pausini pop
Gianluca Grignani pop
Pupo pop/rock
Nomadi rock
Marracash rap
Latin
Enigma gregorian chant, new age
Era gregorian chant, new age
Diablo Swing Orchestra avant-garde metal
Gregorian pop, rock, gregorian chant
Ista hip hop
Dr. Ammondt rock (Elvis in Latin!)
Russian
t.A.T.u pop
Fleur neofolk, pop
Тролль гнет ель folk rock/metal
Arkona folk metal
Ariya metal
Diana Gurtskaya pop
Zemfira rock
DDT rock
Agata Kristi rock
Kino rock
Krematoriy rock
Vitas "opera pop"
Spanish
Manu Chao punk, rock chanson, salsa,reggae, ska
Ska-P ska
Shakira pop
Aventura bachata
Makiza hip hop chileno
Tiro de Gracia hip hop chileno
Control Machete hip hop mexicano
El Guincho tropicália, psychedelic pop
Juanes rock
Héroes del silencio rock/metal
Mägo de Oz folk metal
Swedish
Abba pop music
Finntroll folk metal (from Finland)
Welsh
Cerrys Matthews