Most airlines are certified for ILS, LOC, LOC BC, and VOR approaches. Many also have GPS approach certification now. Some also have NDB approvals. Just depends on the operator and the authorizations granted by the FAA (Based on training and equipment standards).

This is the list of approaches my former pt 121 employer was authorized when I was hired:

ILS, ILS/DME, ASR, DLA, LDA/DME, LOC, LOC BC, LOC/DME, NDB, NDB/DME, SDF, VOR, VOR/DME, LOC/DME BC, GPS OVERLAY