MacBook Pro / OS X Lion
Obviously, if there was a well-known way around passwords that you could just apply, then there would be little point in having them. 

There are several different types of password:

Firmware Password
If you see a prompt almost immediately, then that's likely to be a firmware password. 

User prompt
Normally, the OS loads and then asks for a username and password. 

FileVault password
Sometimes, the OS asks for a password in order to access the encrypted disk.

There is also your AppleID name and password.

It sounds like you're talking about a disk encrypted with FileVault.

Most of these will involve contacting Apple to sort out. You will need proof of your ownership.

Do you have a backup that isn't encrypted? If so, then you can wipe the disk and restore the backup. That will work for a FileVault protected disk.