In the United States there are only a few types of spiders that may raise concern -- most commonly the Black Widow (jet black with a red hourglass-shaped mark on its underside) and the Brown Recluse (violin-shaped marking on its head). The Black Widow tends to cause muscle spasms or cramps, but not much local tissue damage at the site of the bite. In comparison, the Brown Recluse tends to cause significant swelling, blistering, and bluish discoloration at the bite site.
With any bite, good local care is always recommended, including cleaning the area well, applying ice compresses to reduce the swelling and spread, and monitoring for any unusual complaints. Capturing the spider in a jar may be useful if you do seek medical care. Antivenin (a substance directed against the venom of a specific spider) is available for the Black Widow and Brown Recluse. However, antivenin can itself cause significant reactions, so judicious use is always recommended. If you have any concerns, call your physician or local poison center for specific advice.