There was a freaking awesome chrono trigger remake in progress that was full 3d. It got slapped to kingdom come.
It really is a tight-rope subject - its sometimes possiable to balance along it but more often that not you're gonna fall off. Theres many types of fancreations - people with music talent like to remix game music from games they like (www.ocremix.org) - artists draw pictures or comics, writers write fanfic. Unfortunatly for programmers making a game is taking it a step further even if at heart its based on the same principle as other fan creations.
Thing is if that chrono trigger remake, for example, was finished then alot of people who MIGHT of bought an old copy of chrono trigger no longer would bother. Now thats REALLY stretching it as the original chrono trigger is so old. The problem really is that hobbiest/indi game devlopers are getting GOOD. Its damn hard to match latest technology, but even that we are getting closer and closer to (take dbp;s shader support). The risk for the game company is that a fancreation might actually turn out BETTER than their latest effort. Imagine if that chrono trigger remake turned out to be the best thing since sliced bread (and it really WAS looking to be that way, gorgous engine) and when square released a sequel this year a few people played it and then said it wasnt as good as the fan version, which incidently is FREE. Big problems.
HOWEVER - some companies will appreiciate respectful behaviour and return it - not always, but often. IE, find the website of the company who made the game you wish to base a game off, find an email address, write and ask. I know of people who have done this and got a positive response.
I even know one person who got sent a license to allow him to make his remake - oh it was VERY restrictive of course, but enough for him to make his lil contribution.
You should explain your idea and exactally what it is you want to do. I dont mean send them the story, I mean technicalities - do you wish to use their media, whats the intent for the game etc. Most of the time asking for permission to make a small fan-game with no charges and not using any media from the original game will be given an okay. You will obviously have more luck with older, retro, games than asking to remake say doom3. You can ask THEM what they dont want you to do, what restrictions you must adhere to etc.
You will be surprised how far simply asking can get you
