It's been a while so maybe Blizzard took this away... but I used to be able to view my profile on battle.net and see if my Terran won 25% of games, and then say half of those wins were against other Terrans and then some against Protoss or Zerg. Right now I can just see wins by race, but not how against each race. I guess you'd say I want to see all the permutations, so I know what needs work.
The statistics are still there, though they are buried a bit.
Under your in-game profile, go to Ladders, then select Statistics.
There are two types of statistics available:
Race Report shows you your win-loss statistics for each race against each race combo. (Random is not listed, the values are simply noted under the race you actually ended up playing.)
Map Report shows your win-loss statistics for each map.
Both of these reports have data broken out by each of the Starcraft II games, though the Wings of Liberty race statistics are not as detailed.
It looks like Race Report is the one you are specifically looking for.