I like small games ... I am not a fan of whole class games. It's a personal classroom management issue. Most of the games I used were to practice a specific skill.
Games and sites for finding 2-person or small games include these ...
Logarithm Equation game, as students complete a box, they solve the equation and the solution to that equation is their score. My students also played one to practice synthetic division ... a game purchased on TpT.
Five In A Row BINGO ... In this game two students solve problems, claiming squares, trying to be the first to earn five in a row. Here is an example solving square root equations. Another version of this type of game could be played in teams ... but also by pairs ... using powerpoint and linked squares. This example reviews characteristics of exponential and logarithm functions.
Big Ideas Game Closet for middle school and for high school have several games that work well. I especially like the Quadratics Quandary.
We played Risk Your Algebra Skills ... and students were thoroughly engaged! Check out Math Mama's post on the game ... and here's my version.
Math War Games with many variations can be found on Denise Gaskins' site. Check out this link!
This Slope Game looks like a lot of fun!
I especially love Row Games ... not really games but a great way for partners to practice. Students love to see their solutions matching!
What are your favorite two person games??