Why am I seeing serious Wiimote latency on Donkey Kong Country Returns?

Since you mentioned you had latency in two games, I suspect the issue is with the sync itself. Try re-syncing your Wii Remote(s) with the console in the following way:

1. Press the Power button on the Wii console to turn it on.
2. Remove the battery cover on the back of the Wii Remote to be synced. Open the SD Card Slot cover on the front of the Wii console.
3. Press and release the SYNC button just below the batteries on the Wii Remote; the Player LED on the front of the Wii Remote will blink. While the lights are still blinking, quickly press and release the red SYNC button on the front of the Wii console.

Source

As a general precaution, I would also check if there are other devices in the vicinity which might interfere with the Wii Remote's Bluetooth connection. I had an issue where a Bluetooth headset caused control lag for my PS3's controllers, this could be the case for you as well.

Try to set your TV to "Game mode" (or something similar). I had exactly the same problem with Donkey Kong Country returns. Setting the game mode on my Philips TV solved the problem.

After that you should recognize no lag anymore.

The wii's controls are laggy in most games. If you go and play COD on a PC then go back to a wii you'll see it. You hit a button and a slight moment later it responds. Theres lag with all wireless controllers though, and Nintendo needed to have a wired option. Me and my friends tried doing a Super Mario Bros. 1 competition but we all were baffled when we tried doing some fast maneuvering, we all noticed the lag bad. We hit jump and almost .4-.5 sec later mario jumped. We couldnt compensate so we gave up. If you dont notice lag then you need to play on a different system. I wonder if the gamecube controllers would work in these games even though nintendo does not list them as compatible with the game? Also - game mode on your TV only adjusts colors and contrast.