You may want to do things differently on repeat playthroughs of Mega Man X. That's where these passwords come in. Less about simply starting the game at different points, these passwords can let you start at the beginning (after the Central Highway stage) or near the end of the game with or without various collectibles and upgrades.
Passwords cannot save your progress past the start of Sigma Palace 1, so you'll want to do your best to finish off the game from that point. They also won't save your lives, the contents of your sub tanks, or the hadouken, so you'll have to build those up again each time you load from a password.
Start with Leg Parts
Use this password to start the game with the leg upgrade. This gives you a bit more freedom to decide which Maverick you want to go after first.
Start with all Sub Tanks and Heart Tanks
This one will start you with all of the Heart and Sub tanks, but none of the upgrades or Maverick weapons.
Start with all Parts
Start the game with all of X's snazzy upgrades like the Dash ability and improved X Buster. Use them to hunt for everything else yourself.
Start with all Parts, Sub Tanks, and Heart Tanks
Start with every upgrade and collectible. Totally trick yourself out before hunting any of the Mavericks.
All Mavericks Defeated, No Upgrades
Use this password to start with all of the Maverick's weapons and Sigma Palace available, but no Parts, Heart Tanks, or Sub Tanks. You'll probably want to visit each level to collect the upgrades, but this way you'll have a nice big arsenal to play with.
All Mavericks Defeated, All Upgrades and Collectibles Found
Just skip right to the end with everything except the hadouken unlocked. It's more fun to earn this setup yourself, though.