At one time I tried to test my site regularly with all the major browsers, but as browsers have become better behaved, I've switched to validating my code as standard HTML, etc. If I know the code conforms to the standard, then any browser that also conforms to the standard will display it correctly, and typically browsers such as Firefox or IE are sufficiently in conformance to do this. If a browser doesn't conform, that's not my problem. Opera is used by too few people to make any difference, anyway.
Another workable strategy is to keep your site as simple as possible, then it will usually work on any browser. Most of my site is straight HTML, with only one or two pages that contain any scripting, and no ActiveX or Flash or other garbage.