As part of optimising the speed of this site I found a link to Google PageSpeed Insights from their Webmaster Tools page. This is a free service and gives you some great feedback on high, medium and low priority changes you can make to your site to improve response and overall user experience. You can use their web interface and just type in a URL to check the PageSpeed score.
For reference, as of today this site got a PageSpeed score of 94 out of 100, which is excellent.
I also found another good free one, WebPagetest, which breaks down the speed of your site from various locations and allows you to really see which part of your site load is slowing things down. You can do this kind of thing in your browser but the location awareness of this one makes it a lot more useful.