It depends on what exactly you think you see. If you believe you have discovered a new member of a known class of objects — a new comet, asteroid, or even a supernova — you should contact the International Astronomical Union as soon as possible; if your discovery is later verified, you could achieve a certain astronomical immortality, e.g. Messrs. Hale and Bopp!
The International Meteor Organization’s Fireball Data Center tracks meteors and meteorite impacts. The National UFO Reporting Center collects information on sightings of other unusual phenomena.