I have a bow that fits me well. It's a 26" draw with 45# draw weight. Is this powerfull enough to hunt large game with (deer, wild pig, bear)? Or should I look for something with more draw weight?

Should be fine for deer. For pigs, large ones have a shield over their ribs that could be a problem, according to some with more experience. A cut on contact broadhead like a Muzzy Phantom or Magnus stinger should help you maximize penetration.

I would say that you are on the low side of the KE spectrum for hogs.

It will most certainly work if you hit them right (right about what looks like their elbow) on a quartering away shot. However if you make a shot that is not great and hit the shield your penetration will be significantly sub-par and you will have a serious tracking job on your hands.

For deer inside 30 yards, no problem.

As mentioned above, stick with a cut on contact broadhead such as a Steel Force Premium, Muzzy Phantom, or the like. Stay away from anything that will require your BH to first punch through the hide before the actual cutting surface of the blades makes contact (Slick Tricks, Muzzy standards, Thunderheads, etc...)

I've been looking around online at lots of other bows and don't see anything listed at more than 45# on a 26" draw. Am I limited by physics to no more than 45# with that short draw?

I carry short draw bows that go to 70lbs. I will have my 2011 bows in a couple of weeks. And no you are not limited. I will have one a speed bow rated at 350fps that will drop to 25" and another that will drop to 23" these bows are fast, quiet and really state of the art, all made by Darton.