I
never stop supporting browsers. The key is to degrade gracefully in older browsers back to Mosaic 1.0. (Remember that?) You don't necessarily have to provide full functionality or a modern appearance to older browsers, but
you should give them everything they're capable of seeing. That means putting as much in the HTML content as possible. Never use Flash or JavaScript for anything HTML can do.
Of course, there are lots of things Mosaic 1.0 couldn't do. Feel free to use JavaScript if you're doing something that just wasn't possible in 1994. However if you're building an online store or a newspaper website or a blog something else that did in fact exist in 1994, then a 1994 browser ought to be able to read it.