A wedge should have its own identity and not necessarily have the same characteristics as the rest of the irons in your bag. A typical modern wedge system would probably have four wedges; 2 Pitching Wedges (one with 4degs more loft than the other), a Sand Wedge (its design depending on sand type and players skill level) and a Lob Wedge (designed to deliver a high trajectory shot), as with everything in golf there are no standards and the Wedge System described above will differ depending on a player's skill level.
Your wedges should be heavier than your other irons with a greater swing-weight (more weight in the head) to give more feel in the club head and encourage a consistent swing tempo. It would not be unusual for a golfer using graphite shafts in their irons to have a heavier steel shaft in a wedge. The length of the shaft should be the same throughout the wedge system as should the lie angle.
The wedge system should be considered an essential part of your shot making and shot saving game, once you have the right wedges in your bag you should take time out to get used to them. You should at least know the yardage for each wedge with a full, ¾ and ½ swing, this information alone could save the average golfer a couple of shots a round. Should those delicate little shots around the green not be your forte, go and see a good short game coach, he/she will help you get even more from your wedge system.