Here's some games where Star Fox characters or vehicles have appeared briefly. They won't have full summaries but click the images for some (hopefully) interesting info in caption form.
Stunt Race FX (1994, SNES)
After finishing Star Fox, Nintendo and Argonaut used the Super FX chip to create a cartoony racing game. Chunky, polygonal cars with googly eyes race in FULLY 3D TRACKS!! SNES-era Arwings, presumably piloted by members of the Star Fox team, can appear during the game. Thanks to NinDB for the screenshot.
F-Zero X (1998, Nintendo 64)
Futuristic racing game F-Zero X expanded the roster greatly after the limited scope of the SNES F-Zero. Among the many new additions was a character based on Fox's father and with the same name, James McCloud. A not-so-sly reference, or something more? In the Nintendo Power Star Fox comic, James has travelled to another dimension and implies that he has changed form to suit that realm—is that the case here? Eh, probably not. Octoman, also introduced here, migrates to the Star Fox series for "Actual DKU Game" Command. Both of these characters also show up in the sequel F-Zero GX, and in the alternate continuity of the Falcon Densetsu anime and its related games, GP Legend and Climax. It should also be noted that Star Fox elements such as G-Diffusers exist in F-Zero, and that Fox and Falco become racers in a "G-Zero" competition in one of Command's endings.
Picross NP Vol. 4 (1999, SNES)
In Japan, Nintendo Power was the name of a service where you could take a rewritable SNES (or GB) cartridge to have a new game installed on it for a smaller price than buying the actual game. Plus, it allowed different kinds of game to be developed, like a disposable eight-part Picross series. Each one had a set of character-based puzzles; part 4 was the Star Fox 64 set, with the Star Fox team, their vehicles, Star Wolf, and Andross (several 64 games were featured due to this concept being introduced so late in the SNES's life). After completing the puzzles, the picture would become coloured and animated. See part 1 on Foreign Games for the DKC instalment.
WarioWare: Smooth Moves (Again) (2006, Wii)
As well as the usual microgames, WarioWare games often have longer and more involved "boss" minigames. 9-Volt and 18-Volt's stage features the game "Star Fox" (or "Starwing"), where a SNES-style Arwing is flown via simple motion controls through a short stage, and takes on a boss: R.O.B. with a NES Zapper! This has three difficulties, which take place on Corneria, in Sector X, and on Titania's frozen-over form.
WarioWare: DIY (2009, Nintendo DS)
Much more basic than Smooth Moves's boss minigame, this standard microgame has (presumably) Fox shooting down one enemy in a Corneria-like area, in the SNES style. All the content in DIY is made with the in-game editor so the graphics and gameplay in this microgame are very simple.
Steel Diver: Sub Wars (2011, Nintendo 3DS)
This first-person multiplayer submarine game was one of Nintendo's first experiments in free-to-play distribution. Extra subs could be bought with real life moneybucks; one of them added later was the Blue Marine from off of Star Fox 64. Peppy (or some other suspiciously similar talking rabbit) also acted as an instructor; everyone else in the game is human, so he rather stands out. The game was developed by Vitei, a company founded by Giles Goddard, who worked on Star Fox and Star Fox 2 at Argonaut.
Bayonetta 2 (2014, Wii U)
Bayonetta 2 and the Wii U release of the original game added a costume reminiscent of Fox for Bayonetta (and Jeanne) with mini Arwings for guns. Big deal, lots of games have costumes and they're not all on this list. What's more significant about the second game in particular is that if you wear this costume, the fighter jet that appears in the game is replaced with an Arwing, and the way that a whole shooter-type stage plays is reworked to resemble Star Fox 64. At the end of this stage, four Arwings are also visible flying off... who's flying them? (Thanks to superwalrusland.com for the screenshot.)
That was fun, wasn't it? Don't you dare say it wasn't or I'll kick your teeth in.