Tournaments on this site are great, and I think another great addition would be to create Individual Matches.  It would be fun to set up a match with another player, where we play best of 12 games, or first to 6 wins, or whathaveyou.  There could be a variety of options.  This could also be a functionality added on to regular tournaments, where the two finalists play a match of so many games to decide the winner of the tournament, kind of like the World Cup where Gelfand and Ponomariov played 4 games then tiebreaks.

I think that is a good idea, but it wouldn't be so hard to set up manually.

It could be done manually, but so could a tournament.  It's just nice to have an "official" sort of way and structure to do it. 

chess.com already records the cumulative result of the games between any two players e.g.

My Games Against: 13W / 23L / 3D

but it could be worth something to be able to say: "I won 2 out of the last 3".