Running a chat room or a forum is going to take ongoing effort and dedication. They're not hard to set up, but they can be invaded by spammers if they are not frequently monitored. Both can be useful if you want to encourage communication among like minded people, but don't set one up thinking you can then walk away from it.
Chat rooms have a bad reputation. They're portrayed in the media as dangerous places where predators lurk to seduce children. However, a well monitored chat room with a tightly focused purpose can be quite useful to its participants. Chat rooms, however, have declined in popularity since the advent of Instant Messaging. There are still chat rooms around, and you can easily create your own at a site like Paltalk. Just fill in a simple form with information such as the topic of your chat room.
Frequently, chat rooms are used now as part of a larger website, usually for live customer support. LiveHelpEngine.com offers free live help chat, It's great for a company whose customers need help selecting or configuring their merchandise. It's also an efficient way of offering advice or counseling, since a counselor can handle more than one client at a time, answering one while another is typing a question.
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A forum, also known as a "bulletin board", is a means for website visitors to post questions and answers. They're very popular for sharing expertise. A person, for example, needs to know how to plant a tree, so she goes to a gardening forum and posts her question. If it's a popular forum, or one that's actively moderated, she will get an answer within a few hours.
If you have a regular website, you may find your hosting company offers you the ability to set up a forum as part of their offering. iPage, for example, provides blogs and bulletin boards as part of its basic hosting fee. Usually, what the web host is offering is a free program called phpBB3. The phpBB3 bulletin board doesn't require programming knowledge, but it can be a little complicated to set up. Make sure you check the option to have an email sent to a subscriber's mailbox before they can register. Otherwise, you'll be flooded with spam.
There are companies that offer stand-alone bulletin boards. FreeForums.org claim to be free and ad free forum hosting. It's based on phpBB, but they've simplified the interface so it's easier to set up a board.
Again, do not set up a forum unless you are dedicated to monitoring it, removing spam, and responding to posts.