What does one do a web based email situation, where the user doesnt expect to have to enter the password every time they do an operation?

I have been contemplating this for many months, and I am never sure what to search for for the answer.
The way I see it is the password has to be stored somehow either in the page (for a post), in the url (for a get) or as a cookie.
This unnerves me, as the password is stored on the computer (encrypted as it may be) for anyone to access/decrypt and the sole use of web based email for me is to use it from public access clusters (or annoying friends computers who delight in cracking my passwords).
What is the general way to deal with this?
(I hope that made some sense)

In reply to Secure passwords by Anonymous Monk

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.