Scouts are becoming the most popular class today because of their greatest asset: SPEED!!! These guys are FAST, and with everyone else slowed down, scouts are an important part of any TF team. Usually scouts are used for recon or flag runs. Use your scan commands ("scan10", "scan100") to scope the surrounding area, and remember: enemies move. So don't count on them being in the same position that you first scanned them in. Scouts can defuse the Demoman's detpacks also. Just stand on the pack for a sec, then you'll see a message telling you the pack was defused - real helpful for your team. Spies are also exposed when touched by a scout, so inspect all suspicious "team members"; some teams post scouts at the entrances to flag\key areas.
As a scout, use your concussion grenades ("+gren1") to confuse opponents while you fly by them for the flag/key. Flash grenades ("+gren2") can blind opponents for that 2 seconds you need to get dat flag/key. But be careful, your grendaes affect your teammates also!
NOTE: a new trend is developing in TF. "RamboScouts", "PsychoScouts", and "AirScouts". These scouts attack and kill the defense, rather than just running by them. Use your blinding speed to circle-strafe slower soldiers and HWguy's while blasting them with nails. AirScouts are an addition that allows scouts to collect "jump-packs", which let them jump to ridiculous heights. Use these new techniques to dominate opposing teams.

AGAINST

When dealing with scouts, take in account their speed. Always aim your weapons toward their destination, not at them. Try hitting walls, ceilings, and other solid objects around them to try and use blast damage to kill them because direct hits are VERY rare. Against those more militant scouts, use blast damage and grenades to stop them from killing you.