Main contenders: IE8, (IE stands for Internet Explorer for non internet speak people), Firefox, Safari 3.2.3 and the newest addition to the group, Google Chrome/Chromium.
Now for the sake of this article, i am going to talk current versions of the browsers. For IE, this is self explanatory but for Firefox, i am talking 3.0.10 and for Google Chrome, version 1.0.x.
So, without further addoo, here is the order that (i think) the browsers are in order (best first)
1: Firefox 3.0.10

Bad points: Sucks away your RAM and is bad for SSD's, cause it is constant read-write to the drive as opposed to other browsers which run mostly in RAM.
You can get the latest version of Firefox here.
2: Google Chrome/Chromium

Bad points: It's lack of extensions puts it right down the list for me, but the clean user interface and fast loading times bring it further up the list than Safari and IE8.
You can get the latest stable version of Chrome here, and you can follow Chromium (the open source version) here.
Edit: Google Chrome has been upgraded to 2.0. Links above.
3: Internet Explorer 8

Internet Explorer is now famous in the web industry for being annoying. This, however is not because of IE8. Standards that web designers must comply to include being compatible with IE6. This is annoying as it takes extra time and effort to make an IE6 compatible version of the site. But, the latest reincarnation is a wonder for internet browsing. It is based on WebKit, so it is fast. It is also built to be fast. However, it is closed source and so takes a lot longer to produce extensions that cannot be fully integrated into the browser unlike Firefox. It also takes quite a while to load up.
Main page here, downloads available here.
4: Safari 2.3.2

Windows version available here, Leopard available here and Tiger available here.
This is my roundup of all the mainstream browsers at the moment. However, there are plenty of betas out too.
Chromium
Safari 4
Firefox 3.5
These are all massive improvements over their predecessors, however should be used with care. While i believe that Firefox and Safari 4 betas are fine for everyday use at the moment, Chromium development is still in early days and so maybe shouldn't, as it is unstable and could have multiple security problems.
There is that space on the far left of my Windows 7 Taskbar reserved for my browser. While at the moment it is Firefox 3.0.10, it could easily be replaced with Safri 4 Beta or Chrome, as they both fantastic browsers. Chromium is also very promising in the future. Leave thoughts below :)