As a nod to old-school games, I Wanna Be The Guy is littered with references to classic video game series.Warning: Contains spoilers!
In the original game
The game draws perhaps its heaviest overall influence from the Mega Man series. The intro screen is a direct callback to Mega Man 2, and the game features two bosses as well as an area with music and themes taken from that game. Additionally, two very common obstacles in the game - the vanishing blocks and the insta-kill spikes of doom - are ubiquitous mainstays of the MM series.
The Guy's second form is a direct reference to the cyborg boss battle from Contra III, and the Mecha-Birdo fight also possibly references the aerial boss battle from the aforementioned game.
Several regular enemies qualify, as well, such as the birds from Ninja Gaiden.
The music used for the road to The Guy's Castle is the theme from The Moon in Duck Tales, which was likely meant to lead the player to believe that a showdown with the eponymous object is imminent. This being I Wanna Be The Guy, however, the reality of the situation ends up being much worse.
In one of the few references not from a video game, there's a point in a tower climb where you are given two choices of paths to go up. Taking the wrong one results in death by FOOBY THE KAMIKAZE WATERMELON!! (Sadly, without his trademark fanfare.)
In Gaiden
Once again, leaving the game alone on the main screen causes a text-crawl that explains the plot. However, this time, it's a reference to Castlevania 3's opening text crawl.
The file select screen is taken from the ship-building screen from Gradius 3
One of the first obstacles in the level select screen (that isn't Mario based) is the bridge from the first level of Contra. It explodes when you try to jump off of it
The Kid now has the ability to use the Bionic Arm from Bionic Commando to grapple things. The first two levels are based off of levels from Bionic Commando, as well.
On his download page for the game, Kayin notes that the controls are now "Z to jump, X to shoot and C to BIIIONIC AAAARM"