What are the most modern browsers available on Mac OS 10.4
Sorry to resurrect this thread, but the answer has changed since last year. I'm posting this mainly for the benefit of people who will find this thread by googling "modern web browser for tiger". If you still use this computer, I would have to recommend you upgrade from Camino to Omniweb. 

Camino stopped updating their browser a few months ago and has no plans to continue support. Omniweb on the other hand is still being updated and supported and still runs on Tiger. Here is Omniweb running Trello.