Well, topic title says everything :)
What address do you prefer more and why? forum.example.com or example.com/forum?
I'm always trying to use forum.example.com because for me it looks better, but lately with news that Google will be giving better ranks for HTTPS domains I'm thinking about moving to example.com/forum because wildcard SSL certificate is much more expensive.
I prefer domain.com/forum
May be because it is too easy to install in a folder.
I've done it both ways so it somewhat depends on the circumstances. I've used forum.x.x mostly when the forum was on a different host from the main site.
I think users do not tend to enter forum.x x in to the address bar, What they are used to is entering the base site, www.x.x or just x.x and navigate to the forum.
this or they have bookmark to forum home page
I used to be example.com/forum, however lately I have been serving each individual web service on it's own subdomain so I can do different things with SSL.
eg.
with example.com/forum
and example.com/blog
They both have to be SSL if example.com is SSL, whereas:
forum.example.com
and blog.example.com
They both are considered separate entities and can be configured individually.
I currently have my forum completely delivered over SSL, and my blog only has the admin interface over SSL, the rest is standard HTTP. I also don't think example.com/forum is really all that useful unless you integrate all the services (eg have all of the services using the same framework).
Ideally I would like to have 1 software for example.com which deals with forum / blog / everything else (and can import my wordpress / forum / wiki).