WebPageTest.org (free)I tell people about WebPageTest all the time. It allows you to test your website from a server that you choose from a dropdown list. They have locations all over the world to choose from and you can even choose a connection speed to simulate. After the test is finished, you'll get a neat waterfall view showing the elapsed time of every request. It's a great tool to use to observe realistic before & after improvements as you optimize your site.
YSlow has been around a long time. It's a tool that you run locally to analyze a page of your site. It then grades your page and offers detailed suggestions about ways to improve page load times. There are similar tools that have come along since this one. Even WebPageTest does this. But most others I've seen will leave out details and miss important suggestions that YSlow produces.
Fiddler is a neat little tool that allows you to view details of every request and response that goes through your browser. In general, it's a good thing to learn and understand HTTP request and response headers. With time and practice using Fiddler (and a little Googling) you can do exactly that.
Microsoft SEO Toolkit (free)
This one requires IIS to be installed, and it's primarily designed to uncover SEO problems, broken links, and such. But it's neat because it crawls your entire site and it'll also identify slow pages on your site and warn you about it.
Think of New Relic as a lightweight profiler that's designed to gather basic timings on your production code and database. It's detailed enough to be very useful in identifying bottlenecks, but not so detailed as to slow down your production website.
It used to be that CDNs were all designed for large clients and you needed to sign a crazy contract for millions of GB worth of data transfer. Now the prices have come down drastically, and you have services like Amazon CloudFront, RackSpace Cloud Files, and MaxCDN who all have good introductory rates for the little guy. I like MaxCDN in particular because they have all the features I could want, and they perform admirably. By the way, if you have a global audience, a CDN is a worthy thing to invest in. Just use WebPageTest.org to see proof of that.
DNS Made Easy
Again, if you have a global audience and are looking to reduce your global latency, a good DNS provider with IP Anycast routing can help. DNS Made Easy is a great choice as they have a great track record and locations all over the world.