ST (an AT&T Trademark) is the most popular connector for multimode networks, like most buildings and campuses. It has a bayonet mount and a long cylindrical ferrule to hold the fibre. Most ferrules are ceramic, but some are metal or plastic. And because they are spring-loaded, you have to make sure they are seated properly. If you have high loss, reconnect them to see if it makes a difference.
FC/PC has been one of the most popular singlemode connectors for many years. It screws on firmly, but make sure you have the key aligned in the slot properly before tightening. It is being replaced by SCs and LCs.
SC is a snap-in connector that is widely used in singlemode systems for its excellent performance. It's a snap-in connector that latches with a simple push-pull motion. It is also available in a duplex configuration. 
Besides the SC Duplex, you may occasionally see the FDDI and ESCON* duplex connectors which mate to their specific networks. They are generally used to connect to the equipment from a wall outlet, but the rest of the network will have ST or SC connectors.

*ESCON is an IBM trademark


Small Form Factor (SFF) connectors

LC is a new connector that uses a 1.25 mm ferrule, half the size of the ST. Otherwise, it's a standard ceramic ferrule connector, easily terminated with any adhesive. Good performance, highly favoured for singlemode.
MT-RJ is a duplex connector with both fibres in a single polymer ferrule. It uses pins for alignment and has male and female versions. Multimode only, field terminated only by prepolished/splice method.
Opti-Jack is a neat, rugged duplex connector cleverly designed around two ST-type ferrules in a package the size of a RJ-45. It has male and female (plug and jack) versions.
Volition is a slick, inexpensive duplex connector that uses no ferrule at all. It aligns fibres in a V-groove like a splice. Plug and jack versions, but field terminate jacks only.  
E2000/LX-5 is like a LC but with a shutter over the end of the Fibre.
MU looks a miniature SC with a 1.25 mm ferrule. It's more popular in Japan.
MT is a 12-fibre connector for ribbon cable. Its main use is for preterminated cable assemblies.

The ST/SC/FC/FDDI/ESCON connectors have the same ferrule size - 2.5 mm or about 0.1 inch - so they can be mixed and matched to each other using hybrid mating adapters. This makes it convenient to test, since you can have a set of multimode reference test cables with ST connectors and adapt to all these connectors. Likewise, the LC, MU and E2000/LX-5 use the same ferrule but cross-mating adapters are not easy to find.

Connector types

The ST is still the most popular multimode connector because it is cheap and easy to install. The SC connector was specified as a standard by the old EIA/TIA 568A specification, but its higher cost and difficulty of installation (until recently) has limited its popularity. However, newer SCs are much better in both cost and installation ease, so it has been growing in use. The duplex FDDI, ESCON and SC connectors are used for patch cords to equipment and can be mated to ST or SC connectors at wall outlets.

Singlemode networks use FC or SC connectors in about the same proportion as ST and SC in multimode installations. There are some D4s out there too.

EIA/TIA 568 B allows any fibre optic connector as long as it has a FOCIS (Fibre Optic Connector Intermateability Standard) document behind it. This opened the way to the use of several new connectors, which we call the "Small Form Factor" (SFF) connectors, including AT&T LC, the MT-RJ, the Panduit "Opti-Jack," 3M's Volition, the E2000/LX-5 and MU. The LC has been particularly successful in the US.

Connector ferrule shapes and polishes

Fibre optic connectors can have several different ferrule shapes or finishes, usually referred to as polishes. early connectors, because they did not have keyed ferrules and could rotate in mating adapters, always had an air gap between the connectors to prevent them rotating and grinding scratches into the ends of the fibres.

Beginning with the ST and FC which had keyed ferrules, the connectors were designed to contact tightly, what we now call physical contact (PC) connectors. Reducing the air gap reduced the loss and back reflection (very important to laser-based singlemode systems ), since light has a loss of about 5% (~0.25 dB) at each air gap and light is reflected back up the fibre. While air gap connectors usually had losses of 0.5 dB or more and return loss of 20 dB, PC connectors had typical losses of 0.3 dB and a return loss of 30 to 40 dB.

Soon after, it was determined that making the connector ferrules convex would produce an even better connection. The convex ferrule guaranteed the fibre cores were in contact. Losses were under 0.3dB and return loss 40 dB or better. The final solution for singlemode systems extremely sensitive to reflections, like CATV or high bit rate telco links, was to angle the end of the ferrule 8 degrees to create what we call an APC or angled PC connector. Then any reflected light is at an angle that is absorbed in the cladding of the Fibre.