Depending on what I'm trying to accomplish, I have several different adhesives I use.
I mostly use CM Tape Runner. (I tried someone's mini tape runner a few months ago and fell in love with it for tiny pieces. I still need to get one of my own though.)
I also have Xyron - 150, 500, 900. I use whichever size is most practical for the item I'm trying to adhere. This is great for vellum since it's clear and gives complete coverage to the item so there aren't any adhesive lines to show through.
Glue Stick - I basically use a glue stick only for emergency, like when I'm out of tape runner or something. I find glue sticks to be messy and don't always stick items very well or pop loose when dry.
Glue (there are several out there that go on white but dry clear) - I like the thick glue for certain projects but it does take patience since it takes a while to dry.
Tacky Tape or any other thick tape (most of this type have a red liner) - this is great for heavier embellishments, when you have a surface you want to coat in glitter/sand/etc, or for clear objects.
I'm sure there are other adhesives I use from time to time, but these are the main ones.