Writers Online has a number of competitions - the open ones (i.e. non-subscribers can enter) are found here. If you are very quick then you could enter the 750 word short story competition, but the deadline is tomorrow so this is only useful if you already have some micro fiction and a spare afternoon today to polish it! There is also a horror competition (which my friend Simon made me aware of), open until mid-May.
May is also the deadline for the prestigious Bridport Prize. As well as the usual poetry (42 lines max; £7 entry per poem) and short story (5,000 words max; £8 entry per story) categories they have added a new flash fiction category for stories of 250 words or less (£6 per entry). Can you condense a story to that size? It is an impressive skill to have.