Well, there are lots of chess set designs that resemble other games, for instance the Fantasy set resembles D&D.
Videogames that Resemble Chess
Basically everything in the turn-based tactics genre. http://en.wikipedia.org/wiki/Turn-based_tactics

internet blitz and bullet chess resembles chess some.
pfff please, bullet it as far from chess as you can go before it becomes shortbread
Hi, I think this is the closest place I can get to mention our game without annoying anybody :)
Aerena is a turn based PVP game where 2 players place Champions with unique movement and striking patterns on a 7x7 grid based board. Often referred to as 'Mix between Chess and Magic the Gathering' or 'like Battle Chess' and generally attracting a playerbase that also enjoys Chess (Almost all out Season Winners and Tournament Winners told us they were avid Chess players at some point or still are) I thought I could very well mention this on a forum where exactly this kind of preferences are very likely to be met :)
Aerena can be played on Steam (PC, Mac), Android and iOS.
If you want to try the game on PC without spending cash, just let me know here :) On tablets it is free.
Cheers!

Way back in the day, we played a game called Archon on the Apple II. Take a look: http://en.wikipedia.org/wiki/Archon:_The_Light_and_the_Dark
Hard to believe that Archon is an EA title.
Another game that came to mind is:
Duelyst:
http://duelyst.com/
probably the most chess-like and also aesthetically most interesting games coming out 2015!
Just received my beta access today, it is great.
Also, here is out gameplay video:
https://www.youtube.com/watch?v=CPdI9gUQJDs
don´t let the cheesyness of the lore fool you, with 16 Champions, 40 special cards, and 5 kinds of Ships (King), played on 9 different layouts, it is actually pretty complex.
What videogame resembles chess the most (besides the ones that are chess, of course)? Which characters/units resemble chess pieces- in movement, ability, etc.?
My suggestions are:
Advance Wars
Fire Emblem
....... any others?