Sorry for being a bit late with this; the holiday season can be pretty hectic for me. Anyway, these are the currently confirmed games coming out in North America sometime in January. All dates are subject to change, and any system not mentioned does not have any scheduled releases this month.
Nintendo 3DS
January 9th
Chibi-Robo! Photo Finder (digital only)
January 14th
AeternoBlade (digital only)
Wii U
January 9th
Cocoto Magic Circus 2 (digital only)
January 10th
Wii Fit U
PS3
January 14th
Assassin’s Creed Liberation HD (digital only)
January 28th
Dragon Ball Z: Battle of Z
PlayStation 4
January 7th
Don’t Starve
January 28th
Tomb Raider: Definitive Edition
PS Vita
January 28th
Dragon Ball Z: Battle of Z
Xbox 360
January 15th
Assassin’s Creed: Liberation HD
January 28th
Dragon Ball Z: Battle of Z
January 29th
Rekoil: Liberator (digital only)
Xbox One
January 28th
Tomb Raider: Definitive Edition
More may be coming out that has yet to be announced, and any game can be delayed. Hope something you want is releasing this month!