Trip Weapons

The only advantage to trip weapons is that if you fail your trip attempt by 10 or more, you have the option of dropping the weapon instead of tripping yourself:  You dont get to deal damage AND trip.

Trip Weapons: If you want to make a trip combat maneuver, do you have to use a weapon with the trip special feature?

No. When making a trip combat maneuver, you don't have to use a weapon with the trip special feature--you can use any weapon. For example, you can trip with a longsword or an unarmed strike, even though those weapons don't have the trip special feature.
Note that there is an advantage to using a weapon with the trip special feature (a.k.a. a "trip weapon") when making a trip combat maneuver: if your trip attack fails by 10 or more, you can drop the trip weapon instead of being knocked prone.

On a related note, you don't have to use a weapon with the disarm special feature (a.k.a. a "disarm weapon") when making a disarm combat maneuver--you can use any weapon.

Note: This is a revision of this FAQ entry based on a Paizo blog about combat maneuvers with weapons. The previous version of this FAQ stated that using a trip weapon was the only way you could apply weapon enhancement bonuses, Weapon Focus bonuses, and other such bonuses to the trip combat maneuver roll. The clarification in that blog means any weapon used to trip applies these bonuses when making a trip combat maneuver, so this FAQ was updated to omit the "only trip weapons let you apply these bonuses" limitation.

—Sean K Reynolds, 03/15/11