Seven men were arrested this morning, and police vowed to find five more they say are involved in the operation. Commas separate two modifiers of equal weight that describe a noun. Meteorologists forecast another cold, dreary night in Pittsburgh. Parenthetical expressions, which are similar to theatrical asides, require commas because they are transitions and lead into the main clause. Some council members, you may recall, didn't want to appropriate the extra money for two new parks until residents demanded it.
Dependent clauses require commas to be set off from the main clause.
A good example of this is attribution. The study, researchers claim, will change the way drugs are administered to AIDS patients. This is a comma splice. The mayor decided to visit the residents, because she needed their votes. Because is a conjunction that introduces a dependent clause.