Titebond III or if it's a big glue and outside - then it's Cascamite.
D3 (cross-linking) PVA for exterior and interior use, which is similar to Titebnond 2 but more readily available in Europe. Like you I use Cascamite (plastic resin or UF = urea formaldehyde) glue for exterior wherever possible but requies exact joinery work and the assembly needs to be in cramp for 24 hours. Still, it was good enough for the "wooden wonder" (Mosquito aircraft) it should be good enough for me!
I do sometimes use PU (polyurethane) glues such as Gorilla glue for quick jobs where I need to get the cramps off quickly, for example in order to complete stuff to a deadline. The major disadvantages are that it foams if inadequately cramped up (or if the joints are poor), it won't cure in very cold conditions, the foaming squeeze-out can be difficult to remove, the joint stength seems generally lower than a cross-linked PVA and if it gets onto your skin it won't come off easily. It turns the surface of the skin black and it can take a couple of days for the most stubborn bits to loosen up (by natural skin growth/perspiraton) to be removed with a strong soap (such as carbolic), hot water and a pumice stone. I sometimes use the white "stick" PU which can be delivered by a caulking gun, but poor availability/price make it only an occasional choice for me. Main advantage over the runny PU as others have said is that it doesn't foam (although it still turns the skin black)
Can't really be bothered with epoxy. Very messy stuff and extremely expensive. To date I haven't come across anything which required it, but then I don't build boats
Phil