Well let's see, the main centers of gravity for european comics seem to be:
* French-Belgian scene
* Italian scene
* Underground comics, I believe scandinavians are most distinguished in that field, but it's done everywhere.
I do believe that there is a distinguished British scene too, but other than comedy magazines like Dandy or Beano that carried stuff line Bananaman and, well, Judge Dread, I don't know much. As you know, a lot of Brittish creators, specially writers, work in USA comics, but they must have started somewhere, right?
Most of Europe gravitates towards France (It's French-Belgian school seeing how plenty of most important authors are from Belgium). A lot of authors from Netherlands (Van Hamm), Spain (Aster Blistock authors, Alphonso Font), Italy (Hugo Pratt) but also scandinavian or east-european countries work for french publishers and are published primarily for french audience. This is possible because in France, comics have a status of serious, ubiquitous literature and it's not uncommon for people to have large libraries of distinguished comics. It's a large audience despite the fact that it's primarily based in french language zone.
Other european countries follow the french scene at least as much as american, but there's generally not as wide interest in comics as in France. Nevertheless, in ex-Yu for instance, characters such as Asterix, Lucky Luke, Spirou, Jeremiah, have always been more popular and published more often than any of marvel characters.
French-Belgian comics are usually published in graphic-novel format of 45-60 pages, A4 format, hardcover, that we here call albums. Sometimes they're serialized in magazines first. From what I gather, it's typical for a series to have one or two albums published each year. I see that in USA albums are usually published gathering three or five in one book and shrinking them to smaller page format
Most of french-belgian school is based on legacy of two competing comics: Tintin (by Herge) and Spirou (by various, mostly Franquin). Two distinct drawing schools developed as assistants of creators of those two comics went on to create their own works. Most well known successors to Spirou might be Asterix (Uderzo, Goschiny), Lucky Luke (Maurice, Goschiny), Smurfs (Peyo) and, well, Gaston and Marsupilami by Franquin, author of Spirou; the most distinguished successor to Tintin was Blake and Mortimer (Jacobs), but you see echo of his clear line style in many american indy comics too.
But not all french comics are funnies, check out for instance long-running Tangie and Laverdir, or Blueberry and John Difool by Jean "Moebius" Giraud. French scene was a fertile ground for authors who developed their idiosyncratic style that doesn't belong to any particular school, in fact I'd say that most comics belong to that group. Check out works by Hugo Pratt (Corto Maltese), Jacques Tardi (Adelle Blanc-Sec), Herman (Jeremiah) or, more recently, Lewis Trondheim (Les Formidables Aventures de Lapinot) and Joan Sfarr (Rabi's cat).
Thanks to legacy or Spirou and Tintin, most of comics belong to a genre of wide-scope adventure with elements of comedy, very often appropriate to all ages. However French scene is very accepting, French in general seem interested in foreign things: it might be the only country where a wide mainstream audience could embrace Marjana Satrapi, what with her style and themes.
French also have very commercial comics. I understand that the most commercially successful authors nowadays are Van Hamm who writes james-bond-like ultra-macho action comics, and Jodorowsky, who is nowadays writing numerous spinoffs of John Difool, which he wrote several decades ago. Most of commercial french comics are published by Soleil (I believe that Marvel publishes some of it's output), they're also sort of adventure comics, usually set in fantasy or sf enviroment, usually very shoddily written and second-rate even compared to american commercial things, but usually with very slick, ready-to-consume art styles.
One thing that is also typical for french scene is their love of transgression. Topics elaborated in comics like Aster Blistock or John Difool and spinoffs would typically include incest, trans-gender, patricide, extreme violence and sex. Horror elements from american comics pretty much seem prude compared to what you can read here, and it's all pretty mainstream. French don't have the "think of the children" mentality and they don't care to make their comics "appropriate for all ages" the way americans do.
Italian scene is pretty similar to italian films, if you've ever followed output of film studios like Cinecitta, you know that it's working method is making cheap copies of whatever is popular in usa, and making it in huge quantities. A typical serial has a book published every month, and it's up to 60 pages so you may imagine that quality of writing and drawing is not an issue for them. It fact, most often serials are being done by several teams of writer-artists, so it's typical for each episode of a series to be drawn in a distinctly different style.
When I was a kid most of things coming from them were old-school, lone-ranger-type westerns, in the meantime they've caught up with horror and new-age fantasy genres, and somewhat modernized drawing styles to mimic currently popular american artists more.
Despite the fact that most of actually worthwhile italian authors go to work for french instead of churning out these, a few of them did became distinguished. Ticiano Sclavi, creator of Dylan Dogg, has some level of recognition, as I understand.
The greatest that italian school produced might be Alan Ford, whose early run of 100 episodes is truly great. Also great is work that italian studios did on Disney characters, it's always very recognizable by a very stylish art. I'll choose something from italian Disney over Carl Barks any time. Extension of this is Disney's franchise W.I.T.C.H which originated as italian comic strip series.
I understand that spanish scene has similar approach to italian, except in smaller amount. The great comic author Carlos Gimenez worked on cheap paperbacks for years.
Underground comics are made all over Europe, and they're not too far off from what, for instance Jim Woodring does. They often trade in shock and gross-out, they're often drawn in heavy, art-brute style, and we're usually talking about short stories, up to several pages, which can be collected in magazines or fanzines. I understand that most well known of this sort is norwegian author Jason, who is published by Fantagraphics, but he is also considerably tamer and more accessible than most of this type of comics.
As for yugoslavian comics, most of the way we tried to keep our step with the rest of the world, so even before WWII you had comics that were very blatantly ripping off, for instance, Disney comics. For most of existence of Yugoslavia, we were largely influenced by french school, things like Herman or Moebius. There were a lot of WWII comics produced by studios, and I think those were the most popular comics at the time, not the kind of thing that interests me other than as the record of the time when you could draw a brave partisan kill ten nazi germans with one bullet and not blow anyone's suspension of disbelief.
In 90ies we started doing a lot of underground of various kind, and I think lots of it was relevant in european underground scene too. Slovenians in particular had a few long-running magazines, though they were publishing authors from entire region. Our Aleksandar Zograf has been published by Fantagraphics, he tends to write either about dreams or about experiences of living in Serbia, I recommend a lot.
Also since 90ies, I think that influence of french comics has diminished and that of american comics grow. Whenever there's an attempt to make a mainstream comics nowadays, it's usually mostly influenced by american comic books. Also, noone here lives from comics unless they're working for french or americans.