Characters are always wandering off and getting lost. At least that's how it seems when reading forum posts and Account Management (and Tech and In-game) inquiries. There are two common reasons for this (besides the "my girlfriend/wife/husband/boyfriend was mad at me and deleted my characters" option).
The first is that you could be on a different server. Characters are always specific to the server they are created on (unless you move them with a Premium Services World Character Transfer, and then they are specific to the new server). To be sure you are on the right server, you can simply log into each available server and see if your characters are listed. To be sure you're checking all the servers, it is best to make a list and check them off, as they do re-arrange themselves with the most recently visited at the top of the list.
You can also log into my.lotro.com and look at your list of characters and associated server. Also, you can log into the forums, click the "User CP" button and then look at the characters available as avatars. Please note that these options may not display the current server if you have ever moved your characters.
The second is that you are logging into the wrong account or subscription. Characters are also specific to an individual subscription on a specific account. If you use a different username or select a different subscription nickname when logging into the game, you may not find your character. Be sure you're spelling the username correctly. If you have more than one subscription for LOTRO on that account, be sure you're picking the right nickname to log into.
If you can't find your characters on any server, and don't know or remember a previous username, or upgraded the wrong account/subscription, please contact the Account Managment department. They will be happy to research the issue for you. Contact options are located in my signature.