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.)
