There are 9 different services ("branches") of the Imperial Military.
The detailed part...
Battle Station Operations - Operate and maintain the Death Stars (+ other siege weapons in Legends)
Battle Station operations operated and maintained the first Death Star, and would have maintained and operated the second Death Star (if not for a number of rebels). Within Canon, there were a number of (mostly) self-explanatory subsections of this branch - Engineering, Logistics, Maintenance, Personnel, Security, Station defenses, Technical Support.
Imperial Academy - Train and enlist regulars and officers
This branch recruited and enlisted all personal for the Imperial Military. There were a number of institutions that specialized in each branch. Notable students include Biggs Darklighter and Mitth'raw'nuruodo (commonly known to us as Thrawn).
Imperial Army - Ground forces
Sub-units of this branch include:
Due to a lack of content, it is not clear where the regular non-stormtrooper soldiers fit in, but it can only be assumed that they were replaced or part of the Stormtrooper Corps.
Imperial Intelligence - Espionage & Intelligence
Imperial Intelligence (also known as Military Intelligence, IM) were the espionage arm of the Imperial Military. Members of Imperial Intelligence included Death Troopers (as seen in Rogue One) and the Imperial Information Office.
Imperial Marines - Only detailed as a branch of the Imperial Miliary in Canon. Described in Star Wars Legends as Stormtroopers stationed on warships. They are also mentioned as being the units that will board other ships. It can be assumed therefore that these stormtroopers on the Tantive IV are Stormtroopers of the Imperial Marines:
Imperial Navy - Naval forces
Includes sub-branches for starfighters (Imperial Starfighter Corps), the Naval Military Police (separate from the Army Military Police) and Naval Command and Control (which can only be assumed to be the main command of Naval Forces.)
Imperial Special Forces - Special forces command
A term used to describe the special forces units of the Imperial Military. Units that fell under the Imperial Special Forces umbrella included Inferno Squad and the Storm Commandos. In Star Wars Legends, Imperial Special Forces often provided units for other branches of the Military, for example, providing Ghost Battalion to the Army and Imperial Navy Special Forces to the Navy.
Joint Chiefs - Command branch
A command branch of the Imperial Military, divided into Imperial High Command and the Naval chief. Imperial High Command also had a number of sub-sections:
Sector Command - Another command unit
Another command unit, not clear if part of The Joint Chiefs. Members include Commander Brom Titus and Captain Brunson. A sub-unit called Sector Command also existed.