Some people are having trouble logging in. After the Standing Stone logo, you get stuck on a black screen.
A work-around is to rename your Documents\The Lord of the Rings Online folder (e.g., to The Lord of the Rings Online.save). You will have to kill off any LOTRO clients for that to work.
Then start LOTRO normally. It should allow you to log in and enter world.
Exit LOTRO, delete the newly-created The Lord of the Rings Online folder, and rename the saved one back.
I had this problem on one of my computers, but not the other. This fixed the one that was broken.