Some great stuff so far. Well done all.
JRW, I'd include Stav. Its origins might be dodgy, but, even if it has used Japanese arts as a base, it was formulated in Norway and it does have some distinctly European elements to it, e.g. runic stances, traditional medicine, etc.
Anyways, back to the task at hand. I think the first thing you notice when researching European styles is the huge number of wrestling systems. There must be hundreds, but some of the more well known ones are:
Cornish Wrestling - jacket wrestling from southwest England
Devonshire Wrestling - very similar to Cornish except Devonshire wrestlers have an unpleasant habit of using nasty low-line kicks while in the clinch
Cumberland & Westmoreland Wrestling - backhold wrestling from northern England
Lancashire Wrestling - all-in style wrestling; known as catch in the US
Scottish Backhold - closely related to Cumberland & Westmoreland with only a few minor variations
Schwingen - Swiss wrestling style
Ranggeln - Austrian wrestling
Yagli Gures - Turkish oil wrestling
Gouren - Breton style of wrestling; close relative of Cornish
S'istrumpa - wrestling art from Sardinia
Lucha Canaria - wrestling from the Canaries
Glima - Icelandic belt wrestling
Lutte Parisienne - French wrestling style, sometimes taught alongside savate
Collar & Elbow - Irish wrestling style
There's also a fair few stick-fighting styles:
La Canne - French cane fighting
La Baton - French single stick
Jogo Do Pau - Portuguese staff art
Il Bastone - Italian single stick
English Quarterstaff - nuff said
Jagerstock - German stick-fighting
Juego Del Palo - stick fighting from the Canaries
Bata - Irish stick fighting, double sticks is called Troid Da Bata
And then there's all sorts of others:
Zipota - Basque foot fighting; very similar to savate but with more emphasis on jumping kicks
Baratero - knife fighting style of Spanish gypsies
Purring - English and Welsh low-line foot fighting
Chausson - French foot fighting, predecessor of savate although still practiced in its original form in Marseille (Chausson Marseilles)
Le Couteau - French knife fighting
La Panache - French eclectic style of Roger Lafond, founded in the 50s, combining savate and various Japanese techniques
Adresse Francaise - non-contact French kicking style
As setsu said, it's also important to look at the old masters of European fence. In the late mediaeval era, probably the most important master was, as Bamboo has mentioned, Fiore dei Liberi. His
Flos Duellatorum covered abrazare (grappling), daga (dagger), spada (sword), spada longa (longsword), azza (poleaxe) and lanza (spear). There was also Hans Talhoffer's
Alte Armatur und Ringkunst and
Fechtbuch aus dem Jahre 1467 , which between them detailed ringen (grappling), degen (dagger), streitaxt (poleaxe), langes schwert (longsword), and the bizarre hackenschilde, a sort of offensive shield, among many other weapons.
Going into the Rennaisance, there was Achille Marozzo's
Opera Nova, which mainly taught sword and related weapons, and Ridolfo Capo Ferro's and Camillo Agrippa's fascinating rapier manuals. From Germany, was Hans Lebkommer's
fechtbuch, teaching langes schwert, messer (backsword), ringen, degen and stockfechten (staff), and Joachim Meyer's
Gründtliche Beschreibung teaching langes schwert, dusack (wooden cutlass), streitaxt, rapier and ringen, amongst others.
If you want to view any of these books, there are online copies at
http://www.aemma.org/library_top.htm
One of my favourite manuals though is Dutch wrestling master Nicolaes Petter's self-defence text
Klare Onderrichtinge der Voortreffelijcke Worstel-Konst. Although it was published in 1674, most of its techniques are still valid today. There's a copy at
http://www.geocities.com/ulfberth/Petter.htm . Take a look and you'll see techniques resembling aikido, koryu jujutsu, judo and BJJ.
In closing, a word of warning about some "Celtic" arts doing the rounds. Sli Beatha and Comhrac Bas are both systems open to the public in the US that claim Celtic ties, but this isn't the case with either. Sli Beatha at least is honest enough to admit that it is a modern eclectic system, but it claims it bases its principles on Celtic philosophy, whatever that is. Seeing as no Celtic tribe had a system of writing, it's a bit difficult to find out what their philosophy invlolved.
Comhrac Bas is pure fakery though. It claims to be a rediscovered gladitorial form of Celtic origin, but quite why gladiators would be using a Celtic system or just how exactly this system was "rediscovered" remains a mystery.
Also, while researching Celtic martial arts in the past, I've come across mentions of two arts in serious discussion on several occassions, Welsh Llap Goch and Scottish Greenoch, but the record really should be set straight on these. Both are hoaxes.
Llap Goch was an invention of Monty Python, no less, for one of their books. It appeared in a fake ad, a copy of which can be found at
http://www.ppsa.com/magazine/llap.html .
Greenoch was a creation of some of the members of rec.martial-arts newsgroup many years ago. When the inevitable "my style beats all" flames would start up, the members would bring up their study of the ancient Celtic art of Greenoch and how it would kick anybody's arse. Greenoch is, therefore, nothing more than an inside joke...
European Martial Arts/Styles 
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