If you ask ten artists which adhesive they prefer, you'll be lucky if you only get twenty answers. Which adhesive is best will depend on the specific application as much as personal preference. These are my personal preferences.
Acrylic medium is a good, permanent (and non-reversible) adhesive. It dries clear and sticks paper-to-paper like nobody's business. It does have some draw-backs, though. It tends to wrinkle paper. Wrinkling can be mitigated to a large extend by coating both sides with medium and by taking care to make sure the grains of the two sheets match.
A lot of folks use Yes! Paste. It has a reputation for not wrinkling paper, which is good. However, it tends to quickly turn brittle and brown, and turns the paper brown, so I do not use it.
The subject of Yes! Paste has been discussed on Book_Arts-L and elswhere on-line.
I use glue sticks in my composition book journals. Composition books are not archival, so I don't worry much about the longevity of the materials I include in them. I don't use glue sticks in other circumstances, though, because my experience has been that the glue has a high failure rate. I've found that, where I've used it in old sketchbooks, the glue has become brittle and the pasted items have come loose.
More from the Conservation Distribution List.
Tape:I don't use a lot of tape in my work. When I do, it's as a design element, not just as an adhesive. It also tends to be something I use in my journals, where archivalness is not as important to me. I've used everything from duct tape to masking tape to electrical tape, none of which are archival. I've also used linen hinge tape which is archival. I don't have any qualms about using tape, but I think it's important to understand its limitations. Even archival tape will fail eventually, so do not expect it to be a permanent adhesive.
Clear Siliconized Acrylic Caulk:
Caulk is not archival, but it I still use if for some applications. It works well for adhering large and/or heavy items, and bonds to pretty much any surface.
Don't overlook the possibilities of mechanical fasteners. Photos and other papers can be attached using photo corners, brass brads, pins, staples, or photo corners. By wrapping them with wire, larger, heavier objects can be attached to the support. Fabric and paper can be sewn, and small objects can be attached with thread, yarn, or embroidery floss.
Hint: If you don't like the bright, shiny look of brass fasteners, try soaking them for a few moments in undiluted bleach. The bleach will create a patina, and in some cases, will encourage rusting.