Dry Adhesives for scrapbooking, card making, and paper arts are
glue sticks, adhesive runners, and tape.  There are several kinds
of each, but, again, I caution you to check whether it is 'acid-free'
or not.  

There's nothing as fast and easy (although messy) as a glue stick.  
I admit to forgetting to check, but most of the time, I'm using ones
that I know are acid-free.  But for the price, they are great.  They go
on fast, adhere fast, and clean up easily.  They can cover a large
area, and get the job done.  I use a brayer, after I've applied the
glue and set the paper layers together, to roll over and evenly
distribute the glue. It works out any clumps of glue, and runs the
glue out to the edges.  

One glue stick I've recently started using is from UHU.  It's
non-toxic, washable, and acid-free.  This stick goes on purple, but
dries clear - this gives you the advantage of seeing the area you
have covered.  This glue really sticks.  I do use a brayer to even
out the glue and evenly adhere my pages.  Also, if you find you're
having trouble with any glue stick - try putting your hand over the
page for a minute, or sit on the pages.  You're body warmth will
slightly heat the glue and allow for better 'grip' when it comes back
to room temperature.  People have asked about using heat guns
or sitting it under a lamp.  These are doable, but you must be
careful, we do not want to melt the glue - just barely warm it up a
little!

So for something less messy, there are adhesive runners.  These
are strips of adhesive that roll out and you simply run them where
you want them, and put your layers together.  They do require a
semi-steady hand to get them to roll out an even strip - if you're
wavering all over, they're folding up on each other.  You can use
the edge of something solid (a book or ruler) to guide your line - if
a straight one is required!

I've used several, and many work okay.  I recently tried the UHU
glue roller, and it holds better than the 'tape' ones.  This one lays
down a strip of glue and will hold ribbon to paper.  It will hold 2
sheets of cardstock, but textured cardstock would probably be
better held with a liquid glue.

There's no forgetting the usefulness of glue dots and pop dots.  
These double sided adhesives make projects come to life.  For the
record, I have checked all major brands of vellum adhesives, and
sure enough, the ad is right, the only truly clear one is the new one
- Glue Dots - Vellum.  

For quick and easy - I like everyday double sided scotch tape.  I
use it in envelope making, and anytime I need a quick, solid,
straight adhesion.

I know that technically Xyron machines are dry adhesives - but
let's give them their own category.
Dry Adhesives