Being a Cardinals fan for a while, I have a noticeable dislike for playing the Cubs and Giants. As memories start to build, I know from watching many a baseball game that these two teams like to beat us. Weirder still, the TESS inducing Pirates have our number also, without much doubt these 3 teams give us the most trouble in the NL.
After doing some digging, I found some tables that illustrate our record vs each NL team, historically. The most up to date one is on http://baseballalmanac.com, which includes up to 2007. I then simply added on games from 2008 til present, to see which teams we really like to beat, and then which teams give our excellent ballclub trouble.
First, every Cubs fan's favorite stat, is that they have beat us in total wins/losses. We know that much from them, at least. Not many of the other claims such as the Cardinals suck! or the Cubs hit better hold any water. But yes, the Cubs have the regular season wins total vs Cardinals.
vs. Cubs: 1040 wins against 1083 losses (yuck... but pretty close) .490 winning %
vs. Pirates: 1035 wins against 1087 losses (holy f. shit, the pirates are annoying) .488 winning %
vs. Giants: 896 wins against 973 losses (we are worst vs san fran!) .479
So maybe the Giants should be our main rivalry...
Some other rivalries to look at: The Nationals!
vs. Nats: 289 wins against 274 losses (at least we are not losing against them like vs the Pirates) .513 winning %
vs. Rockies: 72 wins against 76 losses (well, I didn't include this because it's a smaller sample and we haven't played them this year) .487 winning %
Without going into this exercise in too much detail, and due to time restraints, I'm not going to go into all the teams we have beat more often than not. But here are the charts that I used if you have any interest in looking at historical rivalries as well as more recent ones: http://www.baseball-almanac.com/teams/teamvsteam-nl.shtml and by year http://espn.go.com/mlb/standings/grid/_/year/2010
From a glance, historically we really have the Braves (we're 4-0 vs them this year, and was 5-2 in '08) and Phillies number (not fairing so well vs Phils in the last few seasons). But all in all, we are basically whoopin ass on those 2 franchises. Also, the Marlins and Brewers usually have not got in our way too much. Finally, we fair pretty well vs the American League in interleague play.