TresSugar.com has put out this list of different types of marriages of convenience:
Immigration: Getting married so one party can stay in a country or gain residency is probably the most common marriage sham. Even I have flirted with the idea!
Cover-up: The marriage could be a beard that's covering up homosexuality or a lie that's covering up, let's say, rampant sex with multiple women. Either way the most detrimental thing about this marriage is usually the only person who knows the "arrangement" is the one benefiting.
Power: Back in the land-owning days, people married to meld fortunes and increase power. Today we still see it when two political, celebrity, or business powers join forces.
Publicity: Whether it's to drum up buzz or distract the public from something less savory, the publicity marriage can spark the media or kill the press.
Health insurance: This is less of a problem now that so many companies insure domestic partners, but marrying to have access to health insurance is as sensible a reason as any. At least, there's usually love involved!
Military: On the barracks you have to live with roommates unless you are married, so why not just love the one you're with. Now!
Protection: This isn't so common anymore, but marrying someone from a marginalized group is a way to protect them from aggressors. This was especially true in Nazi-occupied regions during World War II.