Continuity
Using different scenes to show the same scene or sequence continued
Here edits are used from different angles to show that it is all part of the same fight scene
jump cuts,
An edit which cuts drastically from one scene to another without continuity, showing different angles, different close ups or zoom outs, even different locations.
Here jump cuts are used to great effect in the shower murder scene from Alfred Hitchcock's Psycho, were cuts to different angles match the frenzy of the knife attack, even though no scenes show the knife penetrating the skin
the 180 degree rule
Cutting round from one scene to the other persons perspective
Here is an example of a 180 degree cut in an opening scene from the Avengers: Age of Ultron
Dissolves
Used to fade from one scene to another - often shows change in scene or movement through time
This has been used to great effect in this music video for the song, "Cry" by Godley and Creme.
,shot-reverse-shot,
One scene facing forward cut to next scene facing opposite direction - cut back to first scene facing forward. Used often in conversation or to show quick movement between two people.
Here is an example from Shot/reverse shot in Spider-Man
cutting to a sound-track
Editing down a sequence to match to the best in a sound track or piece of music
Here is an example from who will save you now set to images from Team Fortress 2