Just changed the strings on my Strat (same light strings as usual), but the saddle seems to be pulling up a lot toward the back. I never noticed this before. Any thoughts/suggestions? Thanks.

Saddle? Is that to imply that only one string is doing this? Perhaps you mean bridge?

_________________
"I started out with nothing, and still have most of it"

If the bridge is now pulling up (where the 6 screws are at the rear) then you may have inadvertently gone up in string gauge. If you have then you might want to correct this first. The stock strings when the guitar was new should have been 9-42s.

If you are happy with the strings you just installed its a simple process.
Undo the 6 screws on the rear of the guitar body (the back plate) here you will find the spring claw.

Drop the tuning on the guitar (as you are about to add more spring tension) and then screw in both of the claw screws evenly a few turns to tighten the springs (1/8" will do at first)

Now retune again. The new spring setting should put enough tension to lower down the bridge flush to the body.

Don't over tighten if you don't need to there is no point.

If you still have a gap detune and add more tension as required.

If you have problems getting enough spring tension go to your nearest dealer and purchase another couple of springs. Or you may choose to do a thing called "hard tailing" or "blocking" the trem. See:
http://www.youtube.com/watch?v=xkj8p4Z3Rjg

The guitar is still perfectly playable in floating position. You will need to check that the setup is correct to have the guitar playing as best as it can. This is regardless if you have changed string gauges or now want to have a floating tremolo and use the tremolo/whammy bar. See your manual for how to setup your guitar or numerous how to guides and videos on the web.

If you run into problems you can always pay to have a proper setup done by a guitar tech or luthier. Its best to find someone who is known for good setups as it can be hit and miss depend on their skill.

If you mean saddle, does the screw look to be at a different angle than the saddle itself? If so, that would be indicative of the intonation screw being backed out almost too much (not enough threads holding onto the saddle).