I have a lot of ideas for an OS I want to make someday (but may never have the expertise or time to), and one of my best ideas was for a memory management algorithm. Basically I had (unknowingly) reinvented Doug Lea's algorithm, with the one exception that, because of the way my idea had developed, I was still thinking you'd want to use a hash table to store the next-bin information, when in reality you don't need one at all.

I've also invented a few sorting routines, which may or may not be useful (or even practical), and some of them are variations or crosses between other, existing sorting algorithms. http://inhahe.blogspot.com/search?q=sorting

I also invented a method for finding primes (when i was young) but it's not as good as the sieve of whoever and it's probably obvious anyway. (for every odd number, try to divide by each prime already found in between 3 and sqrt(n). if none divides, add this number to the list of found primes.)

oh, just recently i came up with a way to use SQL to efficiently find substrings within a document. i have no idea if this method is already known.. (i can only post one hyperlink, so i'll just tell you that the SQL algorithm is curretnly on the front page of the aforementioned blog)

here's a Python one-liner I made once for returning all permutations of a string, but i don't know if the basic algorithm behind this has already been done.. i would guess it has.

perms = lambda a: a[1:] and [c+r for i, c in enumerate(a) for r in perms(a[:i]+a[i+1:])] or a