I've got 3, but that's only cause Wordpress and PHPBB all got their own database (since their tables are prefixed I could easly merge them in with my "Multi" database, which right now I think has stuff for 3 or 4 different things in there).
Which brings up my point - you don't need any more than 1 - prefix your tables like WP_Tablename or BB_Tablename or DS_Tablename or Game1_Tablename or Game2_Tablename or SigStat_TableName. Jam them all in 1 if you have to; splitting databases out just makes it easier to back it up but I'd rather have it all in one place anyways.
But on paid I got 10 databases so I might as well use all 10