The next major beta patch for StarCraft 2: Heart of the Swarm will let players start to experiment with a new leveling system. Blizzard promised that it's coming "very soon," and detailed how the leveling and experience systems will work.
According to the Battlenet Blog, you'll earn experience in Blizzard matchmaking modes, and any custom modes played on Blizzard maps. You'll have separate XP bars for each race, which you can level up by playing that race normally: building your own units, and destroying others. Blizzard is also toying with bonus XP perks, set up like mini-achievements. Each race has a maximum level of 20.
Your level will earn you portraits and decals, and your respective race levels will be displayed in your profile so other players can easily see how afraid of you they should be.
But, this is still a beta test, with emphasis on the "test" part. Blizzard says it will probably reset XP at certain points as it makes adjustments. It does note that you'll get advanced warning of the system resets, and may request specific ways of grinding XP to test them out.