The main reason for asking users to register in order to participate in a forum is to avoid spam (in the shape of affiliate links). You will still get spam with a registration, just not as much because it's one extra step the spammer has to go through. Also, your support questions will probably show more 'elaboration', since the person had to invest time in the process of registering. But this is quite relative anyway.
Now, if and once you decide to go for a registration, you face two new questions:
1) Will unregistered users be able to read all the messages and use all functionalities?, and
2) How quick and thoughtful is your registration process going to be? Will you require an email verification? How much personal information will you ask for?
Another advantage of having a database of registered users is the possibility of getting better statistics (not to mention some valuable info about your users). These things can also help you with advertising in the future. And the winner advantage, for me: Email notifications. Users can get notified when there are new answers (but only if you have their email!), and the return rate will be much higher.
But I guess if you don't want them to register but you still want to avoid spam, you can moderate the questions yourself before they are posted.