Three comets will have close encounters with the Earth over the next 2 years; they are the subject of the 4*P Coma Morphology Campaign, an observing program being run by the Planetary Science Institute.
All three comets are very small, ranging in size from 1.2 - 1.4 kilometers in diameter, and are classified as Near-Earth Objects (NEOs) due to their proximity to the Earth. Their comas and tails may not be visible to the naked eye (I hesitate to speculate with them being comets and all...), but they will be observable with binoculars and telescopes, and should be good targets for amateurs and professionals alike.
The Planetary Science Institute is running this observing campaign nearly identically to what they carried out for Comet ISON (C/2012 S1); they are requesting un-enhanced continuum (dust) images, as well as gas (e.g., CN) images with good signal-to-noise ratio, More photography requirements and info can be found at the campaign website: http://www.psi.edu/41P45P46P
"Observations with sufficient signal-to-noise that could be used in any publication resulting from this study will be acknowledged with co-authorship for the observers similar to our publication that resulted from the Global Coma Morphology Campaign for Comet ISON." ~PSI
Comet 41P/Tuttle-Giacobini-Kresak (41P/TGK)
Comet 41P/Tuttle-Giacobini-Kresak will pass between Earth and Mars, closer to Earth. Due to its orbit, and position of the Earth during the encounter, this comet should be visible in the sky for months!
Imaging time interval: End-January through end-July 2017
Jan.30, 2017: 0.434 AU
Mar. 30 - April 3, 2017: 0.142 AU -Closest approach
July 31, 2017: 0.792 AU
Comet 45P/Honda-Mrkos-Pajdusakova (45P/HMP)
Comet 45P/Honda-Mrkos-Pajdusakova will be approaching from sunward, and will be lost in the glare of the Sun until its closest approach; it will be visible for about a month.
Imaging time intervals: Mid-February through mid-March 2017
Feb. 11, 2017: 0.083 AU - Closest approach, but may be washed out by the Sun
Mar. 15, 2017: 0.456 AU
Comet 46P/Wirtanen will pass between Earth and Mars, closer to Earth; it should be visible for several months.
Imaging desired time intervals TBD
Nov. 01, 2018: 0.265 AU
Dec. 15, 2018: 0.0701 AU - Closest approach
Jan. 30, 2019: 0.303 AU