TICalc.org's Program Of The Year polls are open!
For the TI-83+/84+ category, it looks like a bunch of older projects split between two authors-- myself and squidgetx (ticalc profile).

Up for the vote are the following programs (in the order listed on ticalc.org).

Batlib (ticalc link)
Batlib is a huge library for BASIC programmers. It has 120+ functions mostly for graphics and string and data manipulation, list and matrix manipulation, compression, and much more.



CopyProg (ticalc link)
This is a small program that allows users to copy variables from RAM or Archive to another variable. CopyProg2 has a few other features as well (like line reading and reading the names of the variables on your calc). It allows you to do things like copy an archived appvar to a temp program for execution



Embers (ticalc link)
Embers is an ARPG that won Omnimaga Contest 2012. This was a really well put together game. It features good graphics, good AI, and storyline.



FloatLib (ticalc link)
Floatlib is an app that holds many single-precision float routines from addition to hyperbolic tangent. It comes with a built-in reference manual and there are some examples like computing the Mandelbrot Set.



Gravity Guy (ticalc link)
Gravity Guy is "a port/variation of the popular iphone/flash game" of the same name. You basically get to flip the direction of gravity to help navigate obstacles.


LblRW (ticalc link)
LblRW is a small utility for BASIC programmers that lets you read or modify data within the BASIC program, using a label offset. That's a mouthful. Basically, "Hey, I want to store player data in my RPG, let's store it after Lbl PD." Or you can store monster data for quick access for example
(no screenshot, sorry )


StickNinja (ticalc link)
StickNinja was an Omnimaga Contest 2011 entry that earned 3^rd place. It's basically a platformer with awesome Stick Figure and Ninja graphics. Collect coins, destroy enemies; It's got it all.

Okay, added screenshots, thanks!