Fair weather friends, are people who form a bond that is sometimes based on what the other has to offer that will be and/or can be, beneficial to one or the other of them at that specific time. It is a friendship which sometimes is based solely on the phrase "what can you do for me, what can I do for you?" It is not necessarily formed out of a mutual respect, but more times than most, formulated out of a mutual need to keep someone around whom one can depend on for in an emergency, as long as there is some form of commission, so to speak...
The internet friend, someone who was accidentally stumbled upon, makes a connection, knowing the risks associated with it, it still happens.
Open relationships are friendships that are in some way considered a "relationship", usually between two people who come to an agreement that they care about one another, but want to go out and have other sexual partners.
A pen pal is a person corresponded with through the United Postal Service. Someone with which a bond formulates