I would like to create a profile page that shows all of the information that a user has entered about themselves. There are a few fields that I created as well as a bunch of fields that don't seem to have tokens. Is it possible to create custom tokens so that the HTML module can display them? Or is there another way to do this?

you can use TokenReplace in Text/HTML, to display each user the inf0rmation, he has entered about himself including all custom tokens, but Rod is correct, you cannot use it to display another user's data. For this purpose, you can use Links, to specify each user to be listed and link to his user profile, another free module is Effority UserDirectory, latest version provides user profile links as well.