Cyanoacrylates (super glues) are virtually instant, as are some rapid gel glues. Quick-set epoxies are very fast but still require minimal clamping, unless you want to hold them for several minutes! However, while these glues are good for small repairs, they are not good for jobs like furniture assembly. PVAs and polyurethanes need a tight fit, so clamping is important. Also, there’s a risk that the foaming action of polyurethane can push joints apart if they aren’t secured properly.