What an odd question.
There is no need to log in to browse the site but as unregistered buying and selling are not possible you need to log in for these purposes,otherwise how would Ebay be able to register a bid.
I believe fly258 means can you stop eBay from requiring you to sign back in after a certain length of time. I haven't figured out if it is possible or whether my firewall/av config is messing with the cookies.
if you download opera which is a free internet browser, once you log in on my ebay it alows you to save your password etc.so next time you log in instead of typing out your log ins you just click the magic wand icon and presto your in.