Special Characters
When you start a new game and are on the Name Select screen, hold the L button, R button and Select, then press A, B, A, B. You can then use the Control Pad to switch the names to those of the programmers. Or, if you hold L, R and Select, then press A, B, A, B, X, Y, X, Y, you can choose from Star Trek members like Captain Kirk, Mr. Spock, etc. When you're given a password after entering this code, you'll notice that you'll continue from there with a standard cadet instead of the character you chose when entering this code. To avoid this, enter your password, but don't start yet. Enter the above code for whoever you want to play as, then release all the buttons and press Select to resume play. Keep doing this everytime you get a password to keep the character of your choice.
Extra Ships
On the screen where you select what ship you wish to use, hold L, R and Select, then press A, Y, B, Y. This code allows you to choose from the starships Excelsior and Phoenix during either two-player mode or the Combat Simulator.
Kobayshi Maru
Start a new game and go to the "Name Select screen." Hold L, R and Select, then press A, B, A, B, X, Y, X, Y, then choose Captain Kirk. If you reach the final exam as Kirk, you'll be able to hail the Attacking Klingon vessels and save the Kobayashi Maru. When you're given a password after entering this code, you'll notice that you'll continue from there with a standard cadet instead of Capt. Kirk. To avoid this, enter your password, but don't start yet. Enter the above code again, release all the buttons and press Select to resume play. Keep doing this everytime you get a password to keep Captain Kirk.