Unlock Simon Belmont
Unlock Boss Rush Mode and play it once. Reset the machine and during the Konami title screen, press up, up, down, down, left, right, left, right, B, A. Then start up Boss Rush Mode to play with the original vampire slayer! Simon is much slower and doesn't have the fancy moves that the others have. He does hit MUCH harder though, so he isn't that bad of a choice to use.

Play as Maxim Kischine
Enter "MAXIM" as a name after completing the game at least once to play as Maxim Kischine. He is faster and jumps higher than Belmont.

No magic
Enter "NO MAGIC" as a name after completing the game at least once.

Hard mode
Enter "HARDGAME" as a name after completing the game at least once. If you entered the code correctly, you will hear a voice at the start of the introduction.

Boss Rush mode
Successfully complete the game to unlock the Boss Rush option. There are three levels (easy, normal, and hard) that must be unlocked by playing each in succession, starting with easy.

Classic Simon
Unlock Boss Rush mode, then press Up(2), Down(2), Left, Right, Left, Right, B, A, Select at the Konami logo. Select Boss Rush mode to play as the NES version of Simon.

Sound test mode
Successfully complete the game with the good ending (where you rescue Maxim and Lydie).