Just because your website looks terrible in Internet Explorer 6 does not mean you are terrible at CSS. There are several documented bugs in Internet Explorer's rendering engine in regards to CSS. Web designers and developers have been struggling with these bugs for years. Several well known websites like Digg and YouTube are no longer going to support IE6.
You have several options to test your website in multiple browsers. The easiest way is to install all the browsers you want to test against on a local machine. There are 5 major browsers, and they all require different methods to install multiple versions.
Microsoft Internet Explorer
If you are using Windows XP, you can use Multiple IEs to install Internet Explorer versions 3, 4.01, 5, 5.5 and 6.
If you are using Windows Vista or Windows 7 (or Windows XP for that matter) you can download virtual machine images from Microsoft that contain a fully licensed Windows operating system with Internet Explorer. These virtual machine images expire every 90 to 120 days. They offer the following images:
- Windows XP SP3 with IE6
- Windows XP SP3 with IE7
- Windows XP SP3 with IE8
- Windows Vista with IE7
- Windows Vista with IE8
These images can all be used with the free Virtual PC 2007.
Mozilla Firefox
You can install multiple versions of Firefox on the same operating system, but it is highly advised that you create a new profile for each version you are going to install. You can use the steps outlined on Rob Cherny's blog to set this up (the article is referring to Firefox 2, but it works for Firefox 3 and 3.5 too). Alternatively, you can use MultiFirefox.
Google Chrome
There really isn't an easy way to run multiple versions of Google Chrome on the same machine. Chrome installations are user account-specific, and standalone versions of Chrome have been made available (see question 3785991), so you can create a new Windows/Mac user account for each old version of Chrome you want to test.
However, the fact that updates are applied automatically and silently means that you really shouldn't worry to much about designing your website for older versions of Chrome. If this is unacceptable, you will need to use multiple user accounts, or virtual images as advised for Internet Explorer previously.
Apple Safari
Safari is similar to Google Chrome in that there isn't an easy way to run multiple versions on the same machine. Michel Fortin has an article that details how to get multiple versions running on Mac OS X. You can refer to this Stack Overflow question for the lowdown on Windows. Virtual images, again, seem to be the only way to go.
Opera
You can install older versions of Opera without issue, so long as they are installed to different directories.