Here's a bunch of other games that have one of the Arcade/Precursor DK characters popping in briefly to say hello. Not worth a full write-up, but there's a little more info in the captions if you click each picture. Go on, have a click, your mum's not watching is she?
Punch-Out!! (1983, Arcade)
The first instalment of this veteran boxing series, released to arcades, had Donkey Kongs Senior and Junior watching from the audience (they're on the left). Of course, years later Junior got in the ring himself!
Pinball (1984, Arcade/NES)
As stated by a Chad in an episode of The Vine, Pinball for the NES had Mario and Pauline in the bonus rooms, in a mode that more resembled Breakout than pinball. This is the only game with Pauline but without Kongs.
Tetris (1989, NES)
After besting Nintendo's own version of Tetris in some way or another, Donkey Kong Senior can be seen having a little musical jam alongside other Nintendo All-Stars. While earlier (Ongaku Asobi) and later (Tropical Freeze) he favours large strings, here he plays a drum, although a different sort to the bongos his grandson would become obsessed with later.
F-1 Race (1990, Game Boy)
In this simplistic Formula-1 simulator, Donkey Kong Senior again appears alongside other Nintendo stalwarts of the time (GB version only). His role is to cheer you on to the last race, and hang out with attractive human ladies.
NES Open Tournament Golf (1990, NES)
There were lots of golf games released on the NES and Famicom. For this one, Donkey Kong Senior now seems to have a job managing the prize money for the golfing stuff. He's pretty friendly with Mario, it seems. And he speaks English! Is this the first time he's seen communicating in this way? Eh, go ask someone who's a real expert.
Mario is Missing! (1990, MS-DOS)
Luigi's first big solo adventure! He looks wonky as heck, but this image is intended to be Donkey Kong Senior. We know because there are similarly atrocious renditions of other Mario series characters, but only in the CD-ROM re-release version. The SNES and NES versions are even more different, but only this one has a Kong. He now has another job: running a tourist information booth, and again speaking English. Like all the characters, he can appear in various cities.
Tetris DS (2006, DS)
Nintendo went all-out using their IP in retro 8-bit style for this, their final go at a Tetris game. This includes using Pauline and Donkey Kong Senior here and there, as well as theming an entire mode around the original DK Arcade's 25m stage. Push mode is a competitive game, where the screen scrolls away from you and towards your opponent as you clear lines. If the screen is scrolled all the way up, DK and Pauline can be seen on a girder at the top. (Thanks to the blog Spring 2012 IAT 410: Advance Game Design for the screenshot.)
WarioWare: Smooth Moves (2006, Wii)
Other WarioWare games often include some playable approximation of a portion of one of the Arcade Era games. This one, on the other hand, has a cameo appearance by DK Senior alongside other 8-bit sprites in a microgame where "You" (yes, "YOU"!) conduct them playing instruments. DK is again playing percussion, this time something more like a timpani drum. (Thanks to the Metroid Database for the screenshot.)
Nintendo DSi Metronome (2010, DS)
This "lifestyle application" or whatever for the DSi download service had an included minigame where the DSi's microphone would pick up inputs causing Mario to jump over incoming barrels in a simplified rendition of DK Arcade's 25m (because it's always 25m). (Thanks to NintendoLife for the screenshot.)
Well, that was fun wasn't it? I'm imagining you probably scrolled past those images accompanied by that funny organ music from off of the Holy Grail, but that's just me. You can scroll past things any way you like, really, I'm not the boss of you. (Or am I?) (Nope.)