I recommend you keep your account password protected. You wouldn't want anyone having access to your Hard Drive and System, would you? That's a recipe for disaster.
Secondly, you should have 2 accounts on your Mac, both password protected and make one a Standard Account (for everyday use, surfing the web, email etc) and make the 2nd one an Admin Account (for installation of software, making System changes etc).
Having said that, if you want to remove the password just log in and go to:
System Preferences -> Accounts
Click on your UserName in the left collumn and then click on the Change Password button (You may or may not need to unlock the Padlock down the bottom with your Admin password to proceed.)
When the Change Password window opens, enter the Old Password followed by the new one, which you would leave blank in this case. I don't advise this though but it's up to you.
If you want the Mac to log automatically into your account go to the Padlock and click it, followed by your Admin Password. Then click on Login Options at the bottom of the left collumn.
Place a tick in the top box to the right:
Automatically log in as: (Your Username here)
Having finished, just click the padlock to lock the Preferences again and you're done. Be advised that anyone can now have access to your System and this is really a very undesirable situation.
Oh ... and whatever you do, don't turn on FileVault without a parachute .... it can lead to real problems if you don't fully understand the pros/cons. I read a bit about it and decided to leave it well alone as I value my personal data too much and I'm no tech head ....
