These are the clubs where all of the goal scoring players in Euro 2008 were playing leading up to the tournament. Obviously, some of these players will be changing or have changed clubs, but I've used the clubs they played for in the recently finished European season for this list.
# Goals/Club/Players:
8 - Bayern Munich (Lukas Podolski, Bastian Schweinsteiger, Miroslav Klose, Philipp Lahm)
6 - Real Madrid (Ruud van Nistelrooy, Arjen Robben, Pepe, Wesley Sneijder)
5 - Valencia CF (David Villa, David Silva)
4 - Fenerbahçe (Semih Şentürk, Uğur Boral)
3 - Liverpool (Fernando Torres, Dirk Kuyt)
3 - BSC Young Boys (Hakan Yakin)
3 - Spartak Moscow (Roman Pavlyuchenko)
3 - Arsenal (Robin van Persie, Cesc Fàbregas)
3 - Zenit St. Petersburg (Andrei Arshavin, Konstantin Zyrianov)
3 - FC Barcelona (Deco, Xavi, Thierry Henry)
2 - FC Porto (Ricardo Quaresma, Raul Meireles)
2 - 1. FC Nuremberg (Jan Koller, Angelos Charisteas)
2 - A.S. Roma (Daniel De Rossi, Christian Panucci)
2 - RCD Mallorca (Dani Güiza)
2 - Werder Bremen (Ivan Klasnić)
2 - Inter Milan (Zlatan Ibrahimović)
2 - Villareal (Nihat Kahveci)
2 - Chelsea (Michael Ballack)
2 - Galatasaray (Arda Turan)
1 - Baník Ostrava (Václav Svěrkoš)
1 - LASK Linz (Ivica Vastić)
1 - Ajax (Klaas Jan Huntelaar)
1 - Getafe CF (Ruben de la Red)
1 - Panathinaikos (Helder Postiga)
1 - Hamburger SV (Ivica Olić)
1 - FC Lokomotiv Moscow (Dmitri Torbinski)
1 - S.L. Benfica (Nuno Gomes)
1 - Legia Warsaw (Roger Guerreiro)
1 - AC Milan (Andrea Pirlo)
1 - Fiorentina (Adrian Mutu)
1 - CA Osasuna (Jaroslav Plašil)
1 - F.C. Copenhagen (Libor Sionko)
1 - Stade Rennais (Petter Hansson)
1 - Manchester United (Cristiano Ronaldo)
1 - Shakhtar Donetsk (Darijo Srna)
1 - Feyenoord (Giovanni van Bronckhorst)
1 - Dinamo Zagreb (Luka Modrić)
Euro 2008 Goals By League
20 - Spain La Liga
13 - German Bundesliga
9 - English Premier League
7 - Russian Premier League
6 - Italian Serie A
6 - Turkcell Süper Lig
3 - Swiss Super League
3 - Portugal BWINLIGA
2 - Dutch Eredivisie
1 - Czech Gambrinus liga
1 - Austrian Bundesliga
1 - Super League Greece
1 - Danish Superliga
1 - Polish Orange Ekstraklasa
1 - France Ligue 1 Orange
1 - Ukrainian Premier League
1 - Croatia Prva HNL
Interestingly, some of the most represented clubs in the tournament ended with zero goal contributing players.
Clubs with a least 5 players represented with no Euro 2008 Goals:
11- Lyon
7 - Red Bull Salzburg
6 - Steaua Bucureşti
5 - CSKA Moscow
5 - Juventus
5 - Rapid Wien
5 - Stuttgart
Corrections, Thanks to Commenter:
I had missed 2 goals from Wesley Sneijder (Real Madrid) and Arda Turan (Galatasaray) and 1 goal from Thierry Henry (FC Barcelona) in the original post. That of course removes Galatasaray from the no goals list as well. Thanks for the correction.