Drip edge. Why it is critical.
It provides some support to the shingles so that they do not curl down over the years and cause cracking of the shingles and potential water to run down behind the eavestrough. It also creates overlapping of the wooden fascia that can be prone to rot due to water penetration. Another benefit is it can cover any small gaps between the roof deck and the fascia which will prevent animals from seeing an opening which they will then chew at until they are into your attic. Drip edge is also perfect for sealing the ice and water shield to. (Ice and water shield is a water proof membrane that roofing companies install before shingling and helps prevent water leakage in the event of an ice dam.)
From an eavestroughing standpoint drip edge is critical to provide you with a roof that will drain water off the roof and into the eavestrough properly. Unfortunately it is overlooked most of the time.Roofs that are not using a drip edge will often leave the shingles extra-long so that they will sag down into the eavestrough. This will eventually weaken the shingles and hinder proper installation of any new eavestroughs you may be considering after the roof is done.
Most roofing companies that really take pride in their work and want to do the best job will use both Drip-edge and Ice & water in combination. Ice and water is a must if you get a lot of ice build up. The drip edge will ensure that the water always flows properly into the eavestroughs. When using both, the drip edge goes on first and then the ice and water is then stuck down to the top side of the drip edge and followed by tar/felt paper overlapping from button to top. Both items can be very important for having a water tight roof. Having a second layer of protection under neat the shingles is beneficial to every home.
Its still a good idea to have drip edge if you can afford it. Its amazes me how many roofing companies do not promote it more as not having a drip edge is the cause of many long term problems with how water drains off the roof into the eavestrough.