FMCs or FMS' are wonderful pieces of software, in fact, my Master's research will be based on it! I think it is a wonderful addition to the aircraft's cockpit, but it also has its negatives.
Here are some of the positives - much easier for the pilot to navigate from one place to another. In the olden days (not too old), you would have to use the INS to navigate, essentially punch in waypoints, etc and the flight engineer would have to make all sorts of fuel calculations and such. With the FMC, everything is done automatically for you.
Another positive is its flexibility - if for example, there is an inflight emergency and you have to divert to the nearest suitable airport, you can just plug it into the FMS and it will automatically recompute the route, fuel burn, time of arrival etc.
Ability to store frequently traveled routes - the pilots don't have to manually enter in the waypoints, they can just choose the route stored in the database and modify it if need be.
Easier to follow ATC constraints - During arrival or departure you can manually insert restrictions as mentioned above. Much safer as well.
With regards to navigation, almost all FMS use GPS for navigation now a days. VOR, DME
and NDB are also used, but accuracy wise, GPS beats almost everything hands down. Traditional navigation would involve the INS as I mentioned above, but the INS needs to be recalibrated numerous times in order to maintain its accuracy. A good example of the propagation of INS errors may be the KAL007 incident which 'could' have been caused by inaccuracies in the INS.
The FMS also knows how the aircraft wants to fly. This relates to my area of research which involves CDA (Continuous Descent Approaches); the aircraft flies an arrival without any restrictions whatsoever, the main point is the engines are at idle during the entire descent, no level segments unless needed.
Negatives for the FMS: Its not so easy to change an arrival runway! For example, if SoCal TRACON clears you to 25L but for some reason, you have to change to 24L, its requires some amount of keystrokes to change waypoints etc. Could get annoying.
FMS is very very complex! It takes ages to debug and sort through the logic!
Something else to add: ACARS! The FMC also has the ability to use ACARS which is used to send all sorts of data such as aircraft weight, fuel, wind, time of arrival etc to ground stations.
Hope this helps!
[Edited 2007-03-22 23:54:36]