There legal but only if no-one is being charged in anyway shape or form for any part for any of the characters or storyline of these re-made games.
You make as many remakes as you like but they'll never get posted in the DB downloads page or I expect the DB online magazine.
These should be presumed as for your use only and the only reason you would hand them out would be to let people see how good a programmer you are.
You should never also advertise any copyrited stuff in other games of your own that aren't copyrited otherwise you'd never be able sell them comercially.
As far as copying a game idea this is fine as long as its not too close. for example how many final fantasy clones have you seen or 3D fighting games based on the first virtua fighter games.
After all I would presume that all games in some way can be linked partly back to things people have seen enjoyed and adapted for there own use. If you couldn't copy a game style there would be only one turn based RPG (Final Fantasy) and only one racing game (Enduro racer, I think)one space combat game (I dunno star wars arcade?) one scrolling beat 'em up (golden axe?) one sports tennis game (pong? lol) and so on I'm sure you get the idea.
Why not make a remake of your favourite game change the character/ players the scenery and a little of the gameplay to make it unique and voila its not the same game. it may play like it but it isn't the same game.
I myself and working very slowly (so don't ask for screenies or demos) of a 3D fighting game thats a kinda cross between Mortal Kombat and Soul Edge (soul blade to the rest of ya.)
but I don't expect to get in bother for copyright as I'm building the game engine myself and the character models and my little bro is getting the band he's in to do the music. and the final product should be so far evolved that only this posting would give any real idea of where I got the basic ideas from.
So all in all I say
go for it.. don't sell it and there shouldn't be a problem.
Ok so its not a mouse.