Anyone can make suggestions through comments. Here's an example. You'll have to add them to the list yourself but even without that the info is on the page for others. The comments will also become a record of who suggested what, perhaps why and additional information. You'll retain full control over order and can write a bit about each title if you like.
A voting list can be set so anyone can add shows. Order will be based on votes (maybe that will be an advantage, maybe not) and you can't write anything about them.
Anyone who happens by will be able to vote in and add to an open voting list. I don't know if that might be a problem for you. Discoverability of lists isn't great, so it could easily be just your friends. You'll be able to delete shows but won't be able to see who added them.
Will either of these accommodate what you want to do with your list?
