You can try bbpress plugin or you can search wordpress plugin section you can find tons of forum related plugin

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Definitely will be trying bbpress, thanks for the advice =)

I've been testing out different things recently and decided to go with Simple Press. I looked into bbPress quite a lot, and I was looking for a reason to use them because I thought that it would be the most compatible, but in the end bbPress and the bbPress development and the community is just too disorganized at the moment (and it's been that way for a long time - I did this same type of research a few years ago). I decided on Simple Press because the two guys who run it have been active with the plugin (as well as others) for a number of years, and it looks like they aren't going away (in fact, they have new release of their latest version coming soon - version 5). Simple Press, out of the box, does SO much more than bbPress. You might be able to find plugins to help with bbPress, but even if you do, good luck in counting on them being updated.

@Trivum

I've read similar comments at different places so that's why I'm finding it hard to decide. One thing I read is that simple press was integrated into wp so it is really slow if you get a lot of visits. Some people were saying the bbpress is more powerful because it is a separate system or something. Do you have any idea about this?

I need a forum that can use the same user accounts in WordPress, so my users do not have to register twice to start using the forum. And should be adjusted so that I can get it to fit with my own theme.

I prefer simple press.

Why not Bridge it with vBulletin Forums?
vB seems to be one of the best forums out there.

Simple Press is great and very comprehensive, but I've found it hard to upgrade and customize, etc.

Lately, I've been using Mingle Forum - very easy to customize, integrates into WordPress and skinable. See WordPress › Mingle Forum « WordPress Plugins