Very nice! I like the graphical style, character handling and overall feel of the game. A few suggestions:
I'm playing on a Mac laptop so using the up arrow key to jump feels a bit awkward. How about having Spacebar as an additional jump key?
The exit is a bit hard to make out graphically. Perhaps make the exit door brighter or have a shaft of light coming out of it when it has been opened.
When I fell from a high platform onto spikes I lost a life and then respawned where I had last been placed by the knockback. I then fell into the spikes again and died. Perhaps keep the last safe spot (last location the player was standing on a platform) cached and then place the player there after they have lost a life.