As far as international club soccer tournaments go, the undisputed king is the UEFA Champions League. The champion clubs (and several other of the top-ranked clubs) from every top professional league in Europe are drawn into a gigantic tournament every single year essentially to determine the best club in Europe.
The number of teams from each league chosen for each tournament is determined by the UEFA "coefficient," which is a measurement of how successful each nation's professional leagues are in the prior five Champions League and Europa League (kind of like the second-most important club tournament in Europe ... teams knocked out of certain stages of the Champions League are invited to compete in the later stages of the Europa League). The more successful a nation's clubs, the more clubs are invited to compete.
It's an exciting tournament where small teams have the chance to upset some of the biggest names in the world. Most of the time, though, it's the big boys who dominate. For instance, Real Madrid, which usually is one of the richest clubs in the world, has won nine CL titles, more than any other club.