Straight Cigar Cutter - The straight cigar cutter is one of the basic types of cutters which have been in use for a long time ever since it was made. It makes single cut on the cap with a single blade. There are straight cigar cutters which make use of two blades. A straight cut can also be made using a cigar scissor but it is very easy to carry a straight cigar cutter in your pocket unlike a scissor. Also, in case of a straight cigar cutter, the cut can be wherever one intends.
Wedge Cutter - The wedge cutter makes a V cut in one end of the cigars without cutting off the end. It slices from one side and at the same depth every time it cuts. This is one disadvantage as different cigars are off different length and different cap sizes so having a wedge cutter of one size restricts you from smoking different size of cigars.
Hole Punch - The hole punch, as the name suggests puts a hole in the cigars instead of cutting it. There are certain disadvantages in this type of cutter. If the hole punched is not big enough for the cigar, the small passage restricts the path of smoke and the burnt tar also accumulates near the hole giving a bad smoking experience. Also, a hole punch is not specifically needed as something else like a pencil can even make a hole.
Overall, straight cutters with a double blade are the best type of cutters.