A site with this much traffic will be load balanced on a nice, pricey cluster. A low-traffic vBulletin forum can be run off of a single server, though it will need to be optimized. Having a separate webserver and database server in close proximity would definitely be preferable, since vBulletin is hard on MySQL. I am not intimately familiar with vBulletin's internals, but if you can have it use InnoDB tables, do that. This is because MyISAM tables lock up frequently on vBulletin forums, since the entire table is locked during a write. InnoDB avoids much of this because instead of locking the entire table, it only locks the row that is being written to. InnoDB will require more RAM on the database server for good performance, since you want to have all your InnoDB tables cached in RAM for fast reading (innodb_buffer_size should equal the total amount of InnoDB data). On top of this, there's a lot of PHP to run, which takes up a lot of RAM itself. This is what makes two servers a good idea in a lot of cases when the forum is not able to keep up with the traffic. If you have a really high traffic forum, you'll want to multiply that and load balance it. If you're just playing around with having a forum and you do not expect much traffic, you can get away with having it on a single server, but you'll want to be careful. Spambots will find you before a lot of people will. You'll want to make sure captcha forms are enabled for registration, otherwise you might find your small server crashing because the spammers are sucking up all your resources via scripting attacks (also run ModSecurity with a good ruleset - really).
Either way, to run a web site, you want it to be at a respectable datacenter, not out of your own home. You'll get much greater protection from power spikes, as well as power redundancy. You'll get static IPs, which is a must for any site on the Internet. You'll have better security than you can likely afford for your home or office. You'll get a very fast, redundant connection to the Internet, which is very important if you expect decent amounts of traffic. And at a good one, there will be staff there to monitor the server, and get it back going again if it crashes or if one of its hardware components fails.
