I started a lot of games in the last year or two (or three) that I've yet to finish, but the five below are the ones I most want to get back to and "beat" in 2014.
Deadly Premonition (Xbox 360)--It's going to be very interesting to see if I actually go back to playing this one. Although I loved the bizarro story when I started playing it many moons ago, I wasn't so enamored with some of the gameplay (anything resembling a battle scene, basically). Still, I'd really like to finish it someday--if only so I can say I did it.
EarthBound (SNES)--I know, I know--it's wronger than wrong that I've yet to "beat" this legendary RPG. (I've tried three times now, if memory serves.) The thing is, I've loved every second I've played of it during each of my attempts--but something's always distracted me before I could complete it. Hopefully I can avoid that when I go back to my most recently created save file in early 2014.
Final Fantasy: The 4 Heroes of Light (DS)--This situation surrounding this game is a bit strange, as the only thing I have to do is beat its final boss. I've actually battled it a number of times already, and even made it as far as its third (and final, I think) form, but I faltered each and every time. So, I'm going to make another run at it next year--probably after bolstering my party a bit (or a lot).
Fire Emblem: Awakening (3DS)--Another crying shame, right? I can't remember how many hours I put into this title before being pulled away by Animal Crossing: New Leaf, but I know it wasn't close to enough. Hopefully I can give it the attention it obviously deserves at some point during 2014.
Opoona (Wii)--I bought this unique, Dragon Quest-esque RPG with the best of intentions earlier this year, but only made it an hour or so in before walking away for some reason or another. I found the first 60 minutes to be pretty enjoyable, though, so I'll definitely do my best to further explore it in the next 12 months.
Are there any games you guys and gals started in 2013 (or before) and would like to finish next year? Let me know which ones in the comments section below.