Purely singleplayer games, of course, have no need for a forum or messaging system. Games with minimal multiplayer may have the messaging system without the forum; usually in this kind of game the purpose of the messaging system is to send gifts and friend invites or PvP challenges to other players, and optionally the player can type a message to go with this. If your game is part of an existing social network or game stable, they may already have a system in place for this kind of thing. Similarly game stables often have a forum in place outside any of the games where they will create a new subforum for any new game in the stable. And of course there are many free services that will let you make a forum if you are trying to get your game going on the smallest possible budget, though it's not extremely professional looking for a finished game to be using one of these free boards. If you are recruiting a team of volunteers one of these free forums can be helpful to have as a place where team members can talk about developing the game with all conversations being preserved for future reference and there's no need to schedule everyone to be online at the same time. For some purposes or some types of people a voice chat or text chat room may be preferable, and the benefit of real-time communication may outweigh the scheduling difficulty.
One of the few areas of game design where pet games have actually been pioneers is in the incorporation of forum-posting physically into the main game and functionally into gameplay. VPSes and the closely related genre of social gaming sites are some of the only places where game avatars are automatically used as forum avatars and forum posting is rewarded with game currency, as well as a way for players to negotiate trades and other cooperative activities within the game. Some of these sites also make chatrooms available to their players; this part is a traditional feature of MMOs, existing in even text-based MUDs and MUCKs before they evolved into MMOs. (Chat has also long been a feature of networked PvP board games and strategy games.) There may be a chatroom for the whole game, a chatroom for a physical area within the game, a chatroom for people waiting for PvP matchups or trying to recruit a dungeon party, a chat room for each guild or faction, a server for private voice chats within the game, etc.
Private Messaging (aka mail) is usually handled by using the forum system. A private message (note, mail, etc.) is no different from a private forum post that can only be viewed by the sender and receiver. I'm particularly fond of approaches where replies to and from the same pair of people are displayed as a thread, rather than a list of separate mails. Some share a copy between these two people, such that if the sender edits the message after sending, the copy in the receiver's inbox will also be changed. Other systems do not allow messages to be edited after being sent, and may generate a second copy of the message for the receiver (while the original copy goes in the sender's sent box). Some systems have various storage limitations, such as automatically deleting stored messages that are a month old, not having sent boxes, or not saving sent messages unless the sender checks a check box on each individual mail. These economizations are mildly annoying to players, but players may also indirectly benefit from the system not having to deal with storing as much data, so it's pretty much a judgment call.
Some private message systems incorporate the ability to send one or a few items attached to a message. If you want a private message system but not a forum, then you might instead take the approach of starting with the trading system and adding the functionality to comment on an offered trade. An invite or similar request is like sending a trade where instead of an item a clickable link is displayed, which runs a little script to carry out the friend list addition or other request. It's also possible to have private chat messages sent through a chat system as a main private message system instead of anything more like a forum post or email.
There are various commercial forum softwares available, most of which come with a private message system included but may or may not have good chat functionality. Vbulletin is a widely-used example, and one of several that use the UBB standard. I haven't looked into free opensource forum softwares but there probably are some. It's possible to create your own forum system, but you are re-inventing the wheel; I don't recommend attempting it unless you really need your forum to have some features that you can't adapt a commercial software to have. GaiaOnline is an example of a social site that made their own forum software and has integrated several custom features into it over the years, starting with the way players earn money by using the forums and their avatars are displayed by their posts, and then adding signature image automation and regulation, adding the capability to display a car or fishtank, making the banner across the top of the forum interactive, and various temporary forum modifications for events. But the core of their forum software isn't very good, which is most easily visible in the fact that some of their subforums are almost impossible to use due to not handling high traffic well and not supporting thumbnail images beside thread titles. DeviantArt is another example-of a well-known website which made their own forum software and ended up with featureless, user-unfriendly forums. Chat clients are somewhat easier to implement yourself, but again there are an assortment of commercial and free ones available, both closed-source and opensource, and some of them will be more featureful and user-friendly than anything you could make without a lot of time and effort.
So, as a designer you mostly need to plan which of these communications systems you want and how you want to integrate them into the game. Do you want your forum to be usable when your game itself is having server maintenance? If so then you have to plan for them to not be hosted in the exact same place, and probably for user log-ins and money earned from forum use to be hosted separately from the main game.
- Forum(s) [skip if you don't want one]
[indent=1]- [Describe what you want the main game's forum to be like - is there any kind of censoring system, can players block themselves from seeing posts from specific other players, do players earn money for forum use, can players include links and images in their posts, are signature images or text allowed, are forum avatars the player's avatar or something else, does the information below the avatar contain links to a player's collections, property, guild, a view of what items are equipped on the avatar, etc.]
[indent=1]- [If you want to have private forums, such as for guilds or private roleplaying, describe how those should work, such as whether players can have moderator abilities over private forums or threads they create, whether the visual themes of private forums are customizable by players, whether rules about images or signatures are different from those of the main forum, etc.]