For both Firefox and Opera (and even for IE 7) there’s a free tool called Web Developer Toolbar. They are not identical in different browsers (they are also developed by different people :-) but in general they are just toolbars with buttons like
Disable Images or
Sometimes you need to see what is happening
behind the scenes, i.e. what HTTP headers a server is sending. The Live HTTP Headers Firefox extension can help with this a lot. There’s also a similar HTTP Headers Opera widget but IMHO it’s a bit more difficult to use.
There are loads of useful tools out there. In general, you can find lots of accessibility checking tools on the Web Accessibility Initiative Homepage and a number of SEO analysis tools on the RankQuest Homepage. Apart from the usual W3C Validators there are two tools that I use quite frequently. First is the W3C Link Checker and the second is the JuicyStudio’s Colour Contrast Analyser Firefox extension. If you want a non-firefox colour contrast tool you can use AccessColor.