I've heard of many different types of controllers, but I'm not sure exactly what their responsibilities and interactions are.
Here are some examples:
What types of controllers exist and what aspects of a flight is each one responsible for?
In Canada (and I believe similarly in the United States), there are four ratings which can be applied to an Air Traffic Controller license:
Within each of those ratings, the responsibilities are sub-divided a bit based on operational needs. For example, controllers at a tower (with an 'Airport Control' rating) would tend to be qualified in all aspects of tower operations including:
Terminal Controllers (if a terminal control area exists around the airport in question) would be responsible for flights in the immediate vicinity of the airport to approximately 20-50 nautical miles. Their responsibilities may include multiple small airports, just a single large airport, or even just one specific operation at an airport (such as arrival control or departure control). These controllers are usually allowed to apply a smaller amount of lateral separation between aircraft due to the dense nature of the terminal environment and the specific nature of their role.
Once the aircraft leave the terminal (if one exists), the Area Controller-sometimes called enroute control-takes over. They are responsible for anywhere between several hundred square miles of airspace to over several thousand square miles in the case of sectors in northern Canada.
In the case of an aircraft transiting the ocean, a specific type of area controller called an Oceanic Controller takes over. They possess slightly different training in order to safely separate aircraft over the ocean in non-radar airspace.
You can find a nice summary here on the FAA website or here on Wikipedia
But generally speaking,
At an Airport (and this very much varies by airport size!)
Note: if there is no tower at an airport (the case for many small airports) aircraft must self announce on the UNICOM Frequency. It should also be mentioned that some airports have towers that are only in operation some hours of the day, they are considered (if open) un-towered at other times.
There may be a Tower controller (if there is a tower): who deals with airplanes on, to and from the active runways.
There could be a designated ground controller who deals with traffic form the ramp to the runway (at KPNE where I fly the tower handles the ground operations during low load times). They will also handle the movements of other things like plows and service vehicles that may be active on or near the runway.
There may be Flight Data/Clearance Delivery who will give the planes their routes before departure (or any taxiing)
Terminal Controllers handle traffic in the radar terminal area (30-50 miles) from an airport.
Enroute Controllers provide information to airplanes in the air such as IFR instructions or VFR Flight Following (Load Permitting)
You can find the frequencies for the various ATC bodies in the Airport Facilities Directory. You can even listen in live to see whats going on at lots of major airports.
In Europe, an ATCO license contains the following:
An ATCO certificate shall contain one or more of the following ratings:
For each rating, the following rating endorsements are available:
ADV: None
ADI (at least one rating endorsement required):
APP: None
APS (may have one or more rating endorsements, but not required):
ACP (no rating endorsements required):
ACS (can have one, but not two, rating endorsements):
In addition, an ATCO will need a unit endorsement, which is the authorisation to provide air traffic control service for a specific sector, group of sectors and/or working positions under the responsibility of an air traffic service unit. Basically, a certification that you know the local regulations at the unit you are working at.
A language proficiency endorsement is also required in English and, if applicable, in the local language if required.
Furthermore, there are instructor ratings available, but I think that it beyond the scope of your question.
Then of course all controllers need to hold a class 3 medical certificate for their ATCO license to be valid.
As you can see, with the number of ratings and rating endorsements available, there are a lot of different possible combinations. So the answer to "what types of air traffic controllers are there?" is not a simple one. Regardless, I hope the above gives you a general overview of how ATC licensing is structured in Europe.
The previous answers detail the air traffic controller types and their roles very well. However, I find this diagram quite helpful to visually recall the airspace divisions.
ACC: Area Control Center
APP: Approach/Departure Control
TWR: Tower
UTA: Upper Control Area
CTA: Control Area
TMA: Terminal Control Area
CTR: Control Zone
