Planetary Society: Akatsuki is at Venus, Lunar Reconnaissance Orbiter and two Chang'e missions at the Moon, two rovers and five orbiters are active at Mars, Dawn is at Ceres, Rosetta is at 67P, Cassini is at Saturn, and although New Horizons is far past Pluto, it'll be sending back new Pluto science data for most of the year, so I'm counting that as still doing science. By Emily Lakdawalla
'Another two missions (Hayabusa2 and Juno) are in their cruise phase; Juno arrives at Jupiter in August. Two (ExoMars Trace Gas Orbiter and OSIRIS-Rex) or three (if you count the Schiaparelli lander separately) will launch this year, with their science starting after 2016. The Voyagers and other heliophysics missions don't show up on this chart.
'What missions will end this year? Rosetta is the only one with a specific end date, with its landing on comet Churyumov-Gerasimenko in September. Dawn's primary Ceres mission ends in April; it's likely to be kept at work until it depletes its very little remaining fuel, and may not last out the year. Of the seven active Mars craft, four are operating far longer than they were designed to. There's no particular reason to expect any one of them to die this year, but our luck can only hold out so long. I have arbitrarily chosen to fade out the oldest lander and orbiter (Opportunity and Odyssey) at the end of this year, but there's no way to know what the Mars fleet will look like a year from now.
'There is a period in the beginning of 2018 when the only planetary target from which NASA or ESA will be returning science data is Mars. That's sobering. So enjoy 2016's bounty of space missions, because we're at peak planetary.'
Emily's brilliant chart here