CHAMProgramming's CHAMP KONG
http://www.champ-em.com/kong.htm

This DOS-based game looks good, having most of the look and enough of the feel of the original. The four classic Donkey Kong levels—Barrels, Rivets, Elevators, and Conveyor Belts—are fairly well reproduced, and four custom-designed levels (plus a bonus level) are also included. I haven't done well enough to see any of the custom levels, sadly.

Personally, I stink at this version. I find the controls difficult—Mario's position is very specific, and you have to move just right in order to climb ladders, jump, etc. You can't jump immediately after climbing a ladder. Granted, these are challenges; I just can't overcome them.  :-)

The pictures below, and the logo above, were borrowed from CHAMP's site. While you're on CHAMP's site, check out some of their other arcade games, replicating some other great arcade classics.

A reasonably faithful rendition of the Barrels Level.

An intriguing custom level—the girders slant two ways, so barrels roll in both directions. Mario has to really dance to avoid barrels coming at him from both directions.