I had a similar situation. I used to have standing water after big rains at the low end of my house. Unlike you, my house isn't on a hill. It's on the bottom of a slightly graded property although being at the bottom of the grade really hasn't caused me problems. Luckily gravity kept it to one area so it would be isolated if it caused damage. That being said, mine drained rather quickly. I also added a vapor barrier to keep the moisture down where it'd be a little muddy.
My problem was more of my crawl space door and no extensions on my downspouts. Like 80Proof said, go to Lowes and just get some flexible extensions for your downspouts. You can burry them or just lay them on the ground. As for my crawl space door, mine was on the west end of my house which is where the weather generally moves in from. It also was a few inches below ground level so water would puddle up and seep under the crawl space door. The biggest help to that issue was a simple fix. I went and got me 2 backs of quickrete and built the ground up where it didn't slope towards the door. It allowed it to slope back to the yard. I'll still get a minor amount of water, but that can be fixed by simply putting a new door.
Finally, if it's puddling up in one area of the house, you could go in and drill some seep holes in your foundation so it can leak out.
You could also go the more expensive rout and install a drainage system in your crawlspace by trenching out around the interior of the foundation, placing gravel, adding a perforated pipe, covering with gravel, and letting gravity take it to the low point where you could install a sump pump.
French drains would work too but you'd have to do some digging or rent a ditch witch or bobcat. Around the high point of the home or wherever water gets in, dig a trench and do the same as i said on the inside. Go about 2 feet deep, add some gravel, a perforated pipe or a corrugated pipe with sleeve, cover with gravel and tie into the run offs whether it be a down spout or just running it away from your home. You'd obviously want it to be lower on the ends than the center so water will be carried away from the home by gravity.
