fixedthatforyou_fest has compiled the prompts and the list is here. There isn't any claiming, just pick a prompt. Posting will begin on June 12th. More info this way.
spring_renewal is a multi fandom prompt fest that is open for prompting until May 7th. Rules can be found here.
fairytaleinspired, a multi fandom exchange dedicated to giving and receiving fanworks based on fairy tales, fables, legends and myths have opened sign-ups until May 8th. Find out more here.
Finally, marvel_bang, a Marvel centric Big Bang has opened sign-ups for both authors and artists, until July 1st. Find out more this way.