Here is a nice article that talks about some of the many fangames being made or have been made. If anything, check it out for just some possible fangames you might be interested in.
One thing I do want to bring to the forefront though is this:
“Whenever a promising fan game is shown, there are always bound to be a few people who insist on spoiling the merriment with misplaced fears and concerns. Rather than appreciating the talent and ambition being poured into these projects, they worry that “these guys are going to receive a cease and desist,” or insist that “they should use their talents to make original games instead of leeching off the ideas of others.”
To the naysayers, what do you think of fan art? Of music arrangements? Of web cartoons and movies that draw directly from major videogames? How are any of these in any less legal hot water than fan games? The harsh truth is, unless you have received express permission from the license holders, it’s almost always copyright infringement.”
This is pretty much true, and some fangames have been shut down because of copyright infringement and lot of times its because part of keeping the copyright is usually enforcing against any kind of infringement. Which is why you are better off sometimes just coming up with something original.
But then you run into the problem of where you need to innovate or you are a rip-off. I think this is where fan-games shine, because it let’s people be creative with their favorite games, doing what-ifs and stuff like that, without having to come up with some genuine novelty, which can actually get pretty hard.