I often feel while playing that I'm a bit too surprised by things that I should already know. This sometimes causes me to lose games, or at least makes me feel sheepish when I win. Some things that can be advantageous to keep track of, for both yours and your opponent's deck:
Victory Points: I feel that most people try to keep track of this to some degree. I usually do just fine with this, except when alt VPs are on the board. I'll still try to maintain a differential in my head, but when variable cards like Gardens come into play, fuggedaboutit. Even though Isotropic makes it easy, I will also often lose track when VP chips enter the mix.
Terminal Actions: In games with no Villages, I am keenly aware of how many terminals I have. However, when there are Villages, I often lose track of my Village / Terminal ratio, relying on "feel" to get the balance right. I'm sure I get that balance wrong, and I bet if I did keep better track, I'd be able to home in on a proper ratio for different types of games.
Key Cards Balance (opponent vs. you): I'll always keep track of the Minion balance, as well as cursers, Fool's Gold, Governor (how much danger am I in for a Remodeling megaturn?), Platinum (will I win a straight-up Colony buying race?) and a few other cards I deem important.
Total Money In Deck: All right, I'm drawing my whole deck every turn now, but wait... I only have $15 total in it? I guess it only matters in heavy engine games, but I never remember to keep track until I do actually draw my whole deck and am pleasantly surprised or a bit disappointed.
Junk Cards Left In Deck: This applies to games with trashers, and at some point you're able to trash the trasher(s). OK, I guess I'll Bishop the Chapel now - and then my next hand shows me the remaining trash: an Estate and 3 Coppers. I reckon this is not a big deal, since when you're considering trashing a trasher, it's probably done most of the relevant work anyway. But I wonder how many of y'all do keep track.
Cards Played This Shuffle: I'm thinking this can be important with respect to playing Chancellor, buying Inn, etc. Also for Governor/Council Room, if you're deep into your deck and haven't seen your one Militia yet, you could be more likely to play it for +3/4 cards thinking you have a better chance of negating the benefit you give to your opponent. But I rarely have any sense of cards played post-shuffle, but I bet some of you do!
Total Buys/Gains (opponent & you): edited in, courtesy of Rabid. A good thing to keep track of to see if a 3-pile ending is possible, or maybe gauge the likelihood of piledriving something like Silk Road. Also may be useful to estimate what your (or their) Gardens will be worth by the end of the game. I tend to keep track of my own +Buys, but rarely my opponent's...
Overall Deck Composition: I think we all have a rough gauge of this, especially when it comes to key actions, but I'm pretty terrible at keeping track of treasure and specific action counts. This makes it so I never know how big my deck is for Gardens, or how many actions I have for Vineyard. And when making decisions as to buying/playing something like Scrying Pool, having a good approximation of deck composition is probably key.
As you can see, I'm pretty haphazard when it comes to mental bookkeeping. I'm curious to see what y'all keep track of - I also wonder how much it correlates with greater success in the game (as for me, I'm currently level 25 on Iso).