At the same time you can't underestimate the importance of many American bands. What would death metal have been without Morbid Angel, Obituary, Death, etc.? Sure there was the grindcore thing in Europe, but these Florida bands as well as bands like Possessed helped create and define the genre.
How about thrash? Sure there were the direct European influences on the first American thrash bands from bands such as the NWOBHM groups and Motorhead, but it Metallica, Megadeth, and Slayer that really created the entire genre. And Metallica's compositional elements, progressions, and lead harmonies circa '86-89 have not only inspired countless bands and opened the door for more progressive metal acts, but that sound can be heard in many bands today. Check out Godhead's Lament, the guitar harmonies right before he sings "searching my way to perplexion" - straight out of metallica's book.
With that said, if we're talking metal I'd say my favorite European bands other than Opeth are Nightwish, Lacuna Coil, Dark Tranquillity, with bands such as Finntroll, Anathema, and Katatonia also up in the running.
If we're just talking groups in general, I'd have to include mum and Bjork. Also Tete and Autour de Lucie (who I just heard last week but is getting heavy rotation).