On Canon sources, you have 4 classes of ships that have any capabilities of separation between sections of the ship. There are probably 3 that are capable of doing so without assistance.
TL/DR: Constitution (Emergency Only), Galaxy (Dynamic/easily reattached), Sovereign (Hinted to in designs, maybe Emergency Only), and Prometheus (Dynamic/ Multi-Vector-Assault)
Constitution Class: There are design mentions of the ability to separate the saucer section from the engineering section, but there was no implementation of it on TV or in the movies. I believe there was a reference in a Novel that stated that it was for emergency purposes only.
Galaxy Class: We got to see saucer separation right out the gate on the Pilot episode of TNG, not to mention other episodes and the Enterprise-D's only movie appearance in Generations. Michael Okuda helped to create the coolest technical document of all time, releasing an entire Technical Manual for the Galaxy class, Enterprise-D. In this, it details the step by step process, as well as automated emergency procedures that incorporated saucer separation.
Sovereign Class: It was mentioned in more general technical manuals that the Sovereign Class continued the ability of its predecessor for saucer separation. However, it was never demonstrated, and I do not recall any Novels mentioning it.
Prometheus Class: One of the coolest things to come from Voyager, a ship mainly built off the idea of section separation for a numerical tactical advantage in combat. Multi-Vector-Assault-Mode demonstrated one ship wrecking Federation and Romulan ships alike in that episode. This is also the only example known of each section having their own Warp core and warp nacelles.
Miranda, Nebula, Akira, and Runabouts: These classes are supposed to have 'Mission pods' that can be changed out at spacedock, which allows them to have more functions in the long term.
Intrepid Class: That cool 'Aero shuttle' that is docked on the bottom section of the saucer looks big enough to have to count in some way. I'm sad to see that they never showed this off in the TV shows.