There definitely isn't any single definition adhered to by hobbyists. For
me, it's pretty simple, though — in order for a game to be a "roleplaying game" it must have two elements:
1. Roleplaying: Wherein people assume the roles of imaginary characters or beings other than themselves.
2. Game: An activity providing entertainment or amusement by way of adherence to rules.
Any game that has those two rules is a roleplaying game in my estimation. This includes the widly hyperbolic examples such as "My friends and I pretend to be bankers when playing Monopoly and have invted our own rules for character death!" that often show up in threads like this, posted by parties attempting to derail any serious discussion by introducing improbable scenarios.
The good news is that, in such cases, under my own definition I can state with authority that by modifying the way Monopoly is played in three different ways (i.e., first by introducing imaginary character roles, second by having players assume them as personae, and third by incorporating rules that govern them), such folks have
transformed it into a roleplaying game!
Of course, some people will scream that role-playing games do not require roles, or rules, or anything else that the name suggests. I've seen more than a few people argue this and it serves as a great example of why the question "What is a roleplaying game?" will never have a single answer.
To wit, my answer works for me, but some others think that any game which requires measuring character movement on the tabletop is not a roleplaying game. Incidentally, this is, for me, always funny because it excludes all editions of D&D from the category of "roleplaying game" —
every edition of D&D has included rules for measuring movement on the tabletop, either in inches or squares
