Project64- Nintendo 64 Emulator
Project64 is a free N64 emulator for the PC. It emulates several games very well and is still updated regularly.
I have played through DK64 and beat the game with no problems (along with many other games). There are however minor graphic and sound glitches in certain areas of the game, but this has very little impact on game play. I was able to find a USB to N64 controller adapter which worked great with the emulator. Most USB controllers will work and with a USB adapter you can use a Dualshock as well.