I submitted a FOIA request for every contact made by the DSN from 2010 onward (I received contacts from Jan 1, 2010, till Sep 1, 2018)
Here is a summary of the contact time for all 86 Missions contacted by the DSS in that time sorted by total time (in hours).
+------------------------------------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-------------+
| Mission | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | Grand Total |
+------------------------------------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-------------+
| Mars Reconnaissance Orbiter 05 | 10428.6 | 8941.0 | 8740.9 | 9326.6 | 10160.2 | 10085.1 | 9238.2 | 10281.4 | 6468.6 | 83670.7 |
| 2001 Mars Odyssey | 10677.4 | 8850.7 | 8785.9 | 9297.9 | 9588.2 | 8517.0 | 8105.7 | 9914.2 | 6082.8 | 79819.8 |
| Voyager 1 | 6207.7 | 4848.4 | 3608.7 | 6554.1 | 4062.1 | 5056.4 | 3900.8 | 6184.7 | 1735.9 | 42158.7 |
| ISTP SOHO Mission | 6300.8 | 4925.0 | 4498.5 | 4656.9 | 4452.3 | 3853.8 | 4857.5 | 4442.1 | 3066.2 | 41053.2 |
| Dawn Mission | 909.1 | 4555.4 | 5415.4 | 885.8 | 918.4 | 5075.6 | 7755.7 | 2152.3 | 2670.3 | 30338.0 |
| Voyager 2 | 3573.1 | 2741.6 | 2349.5 | 3248.9 | 3072.8 | 3510.1 | 3429.3 | 5616.6 | 2143.1 | 29684.9 |
| Mars Atmosphere and Volatile Evolution | - | - | - | 891.2 | 4449.7 | 4866.6 | 5167.5 | 7405.4 | 4905.3 | 27685.8 |
| STEREO Ahead | 3267.2 | 3350.4 | 3199.6 | 2624.4 | 2654.8 | 2126.8 | 3198.7 | 2638.6 | 2255.5 | 25316.0 |
| Cassini | 3537.0 | 2842.7 | 2988.2 | 3238.4 | 2744.3 | 2933.7 | 3134.9 | 2753.1 | - | 24172.3 |
| Juno | - | 2399.2 | 2190.0 | 3361.7 | 1599.7 | 1707.9 | 5033.5 | 4358.8 | 2535.2 | 23186.0 |
| Chandra | 2538.1 | 2578.9 | 2483.2 | 2492.7 | 2466.6 | 2472.0 | 2514.7 | 2448.5 | 1522.0 | 21516.7 |
| MESSENGER | 1441.8 | 5107.7 | 4372.5 | 4047.1 | 4124.4 | 1252.8 | - | - | - | 20346.3 |
| New Horizons Pluto & Charon | 1309.8 | 1196.1 | 1189.6 | 1664.5 | 1512.3 | 5311.8 | 4532.9 | 1983.6 | 999.7 | 19700.4 |
| ISTP GEOTAIL Mission | 2136.2 | 2126.3 | 2129.6 | 2051.5 | 1986.7 | 1983.2 | 2011.2 | 2002.8 | 1325.8 | 17753.3 |
| STEREO Behind | 3207.1 | 3649.4 | 2872.7 | 2949.9 | 2762.9 | 191.8 | 521.7 | 576.7 | 281.9 | 17014.2 |
| Advanced Composition Explorer | 1985.3 | 1973.4 | 1880.0 | 1862.8 | 1784.7 | 1738.0 | 1888.4 | 1882.9 | 1308.5 | 16304.0 |
| Mars Express | 1657.6 | 1940.2 | 983.7 | 1890.9 | 1572.0 | 1777.6 | 1731.0 | 2254.8 | 611.8 | 14419.6 |
| ISTP WIND Mission | 1409.8 | 1587.9 | 1641.8 | 1590.8 | 1499.3 | 1455.0 | 1555.8 | 1540.7 | 1093.1 | 13374.3 |
| Mars Science Laboratory | - | 1065.7 | 4290.8 | 1506.9 | 1324.1 | 1258.0 | 1241.8 | 1430.6 | 735.6 | 12853.4 |
| Kepler | 1541.3 | 1265.3 | 1309.5 | 1398.2 | 1301.6 | 1145.6 | 1763.7 | 1524.8 | 1162.4 | 12412.4 |
| Spitzer (SIRTF) | 1942.6 | 1269.0 | 2080.0 | 2235.0 | 1095.7 | 1094.5 | 953.0 | 899.3 | 586.6 | 12155.8 |
| Mars Orbiter Mission | - | - | - | 790.4 | 3504.2 | 2440.4 | 1614.6 | 1306.3 | 217.8 | 9873.8 |
| Rosetta | 564.3 | 377.5 | - | - | 2264.8 | 3061.1 | 2495.5 | - | - | 8763.3 |
| Gravity Recovery and Interior Laboratory A | - | 1933.8 | 6722.0 | - | - | - | - | - | - | 8655.8 |
| Gravity Recovery and Interior Laboratory B | - | 2001.5 | 6561.4 | - | - | - | - | - | - | 8562.9 |
| THEMIS B | 1129.3 | 1126.5 | 722.3 | 794.5 | 791.1 | 812.2 | 730.1 | 714.9 | 415.6 | 7236.3 |
| THEMIS C | 1039.4 | 1097.2 | 709.9 | 784.7 | 742.6 | 833.1 | 779.7 | 695.7 | 444.0 | 7126.3 |
| OSIRIS-REx | - | - | - | - | - | - | 1716.5 | 3307.8 | 1629.8 | 6654.1 |
| Deep Impact | 2936.8 | 938.4 | 989.4 | 574.9 | - | - | - | - | - | 5439.6 |
| Lunar Reconnaissance Orbiter | 128.7 | 154.1 | 39.8 | 48.7 | 623.0 | 963.6 | 968.6 | 1223.1 | 821.2 | 4970.7 |
| CLUSTER-4 | 843.8 | 982.1 | 1017.6 | 921.3 | 740.5 | 50.5 | - | - | - | 4555.8 |
| Mars Exploration Rover #1 Flight | 595.4 | 562.7 | 603.7 | 459.1 | 488.7 | 487.3 | 467.8 | 592.7 | 268.7 | 4526.1 |
| Planet-C | 1611.2 | 157.8 | - | - | - | 2255.1 | 448.0 | - | 45.5 | 4517.7 |
| Magnetospheric MultiScale spacecraft 1 | - | - | - | - | - | 1084.2 | 1030.5 | 1146.2 | 797.7 | 4058.5 |
| Lunar Atmosphere Dust Environment Explorer (LADEE) | - | - | - | 2188.1 | 1860.4 | - | - | - | - | 4048.5 |
| Magnetospheric MultiScale spacecraft 4 | - | - | - | - | - | 1002.2 | 889.1 | 1000.2 | 704.1 | 3595.5 |
| STARDUST | 1995.9 | 1533.2 | - | - | - | - | - | - | - | 3529.1 |
| CLUSTER-1 | 675.8 | 776.8 | 644.3 | 642.0 | 684.2 | 99.9 | - | - | - | 3523.1 |
| Magnetospheric MultiScale spacecraft 3 | - | - | - | - | - | 1019.3 | 848.3 | 973.5 | 669.1 | 3510.1 |
| Magnetospheric MultiScale spacecraft 2 | - | - | - | - | - | 1001.6 | 859.8 | 945.7 | 668.9 | 3476.0 |
| CLUSTER-2 | 583.8 | 685.5 | 459.1 | 422.4 | 439.0 | 43.3 | - | - | - | 2633.1 |
| Integral | 2317.6 | - | - | - | - | - | - | - | - | 2317.6 |
| CLUSTER-3 | 247.1 | 449.9 | 583.4 | 506.1 | 207.3 | 32.8 | - | - | - | 2026.5 |
| Hayabusa-2 | - | - | - | - | 284.1 | 321.8 | 366.2 | 38.3 | 636.5 | 1646.9 |
| InSight | - | - | - | - | - | 68.6 | - | 48.5 | 1515.2 | 1632.3 |
| Mars Cube One A | - | - | - | - | - | - | - | - | 1497.5 | 1497.5 |
| Mars Cube One B | - | - | - | - | - | - | - | - | 1482.4 | 1482.4 |
| ExoMars | - | - | - | - | - | 28.0 | 156.6 | 328.9 | 714.1 | 1227.5 |
| Deep Space Climate Observatory | - | - | - | - | 61.7 | 646.3 | 156.5 | 134.8 | 112.1 | 1111.5 |
| MUSES C | 1076.8 | - | - | - | - | - | - | - | - | 1076.8 |
| Mars Exploration Rover #2 Flight | 662.2 | 413.7 | - | - | - | - | - | - | - | 1075.9 |
| Transiting Exoplanet Survey Satellite | - | - | - | - | - | - | - | 23.3 | 683.3 | 706.6 |
| MAP | 702.7 | - | - | - | - | - | - | - | - | 702.7 |
| Solar Probe Plus | - | - | - | - | - | - | - | - | 585.7 | 585.7 |
| Venus Express | 86.0 | 98.3 | 61.2 | 8.2 | 160.5 | - | - | - | - | 414.2 |
| X-Ray Multi-Mirror | - | - | - | - | 46.3 | 112.9 | 112.1 | 87.2 | - | 358.5 |
| Global Astrometric Interferometer for Astrophysics | - | - | - | - | - | - | - | - | 141.9 | 141.9 |
| GOES-S / GOES-17 | - | - | - | - | - | - | - | - | 114.2 | 114.2 |
| Tracking and Data Relay Sat-10 | - | 84.1 | - | - | - | - | - | - | - | 84.1 |
| PROCYON | - | - | - | - | - | 64.2 | - | - | - | 64.2 |
| Tracking and Data Relay Sat-13 | - | - | - | - | - | - | - | 31.0 | 5.1 | 36.1 |
| Deep Space Network | 3.1 | 8.6 | 2.1 | 17.2 | - | - | - | - | - | 30.9 |
| Tracking and Data Relay Sat-3 | 14.8 | 4.9 | - | - | 6.8 | - | - | 2.8 | - | 29.2 |
| Exploration Mission 1 | - | - | - | - | - | - | - | - | 28.9 | 28.9 |
| GOES-P / GOES-15 | 22.3 | - | - | - | - | - | - | - | - | 22.3 |
| Tracking and Data Relay Sat-11 | - | - | - | 19.5 | - | - | - | - | - | 19.5 |
| Tracking and Data Relay Sat-5 | - | - | - | - | - | - | - | 2.3 | 13.5 | 15.8 |
| Tracking and Data Relay Sat-7 | - | - | - | - | - | - | - | 15.8 | - | 15.8 |
| GOES-R / GOES-16 | - | - | - | - | - | - | - | - | 11.4 | 11.4 |
| International Cometary Explorer | - | - | - | - | 11.3 | - | - | - | - | 11.3 |
| Tracking and Data Relay Sat-9 | - | 2.6 | - | - | - | 6.0 | - | 2.3 | - | 10.8 |
| Imager for Magnetopause-to-Aurora Global Exploration | - | - | - | - | - | - | - | - | 8.1 | 8.1 |
| GOES-N / GOES-13 | 8.0 | - | - | - | - | - | - | - | - | 8.0 |
| GOES-O / GOES-14 | 7.9 | - | - | - | - | - | - | - | - | 7.9 |
| GSC3 | - | 7.7 | - | - | - | - | - | - | - | 7.7 |
| Tracking and Data Relay Sat-4 | - | 7.3 | - | - | - | - | - | - | - | 7.3 |
| Advanced Tracking and Observational Techniques | - | 7.2 | - | - | - | - | - | - | - | 7.2 |
| Goldstone Solar System Radar | - | - | - | - | 7.2 | - | - | - | - | 7.2 |
| Tracking and Data Relay Sat-8 | 7.2 | - | - | - | - | - | - | - | - | 7.2 |
| TEST | - | 5.9 | - | - | - | - | - | - | - | 5.9 |
| Tracking and Data Relay Sat-12 | - | - | - | - | - | - | - | 4.3 | - | 4.3 |
| Tracking and Data Relay Sat-6 | - | - | 4.3 | - | - | - | - | - | - | 4.3 |
| GOES-M / GOES-12 | 3.5 | - | - | - | - | - | - | - | - | 3.5 |
| Tracking and Data Relay Sat-1 | 2.5 | - | - | - | - | - | - | - | - | 2.5 |
| DSS | - | 1.0 | - | - | - | - | - | - | - | 1.0 |
+------------------------------------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-------------+
| Grand Total | 81336.8 | 80632.6 | 86130.7 | 75953.2 | 78056.5 | 83847.4 | 86175.8 | 84917.1 | 55722.5 | 712772.7 |
+------------------------------------------------------+---------+---------+---------+---------+---------+---------+---------+---------+---------+-------------+
Here is a link to the raw CSV straight from NASA, as well as the Excel sheet I used for the above calculations (hosted on archive.org)