Without deleting your history files?
I once used Firefox (by setting the history to record 9999999 days of it). But then it suddenly started clearing out my old history files. I went into about:config (and then did a search for everything that contained "history" and maxed out all the settings there), but I'm not sure if I can still trust Firefox to log everything (the places.sqlite file often stops growing - although this could be due to the way it allocates HD space before it actually uses it).
Chrome doesn't really allow access to all your past history (through the ctrl-h feature on your browser), but it does seem to keep archives of your old history files (as labeled by their month). The main issue with Chrome is that there isn't a Nirsoft viewer that you can use like you can with Firefox. Also, philosophically speaking, Google is a lot more into the idea of logging everything.