The next democratic primary competition isn't for another 3 weeks, and while it looks like it's not going to be important (Obama is too far ahead to lose elected delegates, and superdelegates are likely to follow the will of the majority of the electorate, even though Hillary would prefer the delegates vote for her whether pledged or super. Nevertheless, a whole bunch of democrats still get to vote, and here's when:

April 22

Pennsylvania primary

May 3

Guam caucuses

May 6

Indiana primary, North Carolina primary

May 13

West Virginia primary

May 20

Kentucky primary, Oregon primary

June 1

Puerto Rico primary (originally June 7th as a result of a typo)

June 3

Montana primary, South Dakota primary

See all the previous primaries.