Each browser is limited cookies in two ways. The first is a per domain cookie limit that allows a single domain to only store x cookies before the oldest gets erased to make room for the new cookie. The second is an overall cookie limit which erases the oldest cookies when the limit is reached.
The maximum cookies per domain setting usually has impacts on large websites that store lots of cookies on the computer. Remember that domain means that cookies saved from the main domain name but also from all subdomains count towards the limit.
The second limit is not that much of a problem nowadays anymore. Firefox had a hard coded 300 cookie limit back in 2004 which caused some serious problems but most browsers support much more than that so that it's unlikely that users will reach the limit.
Per Domain Cookie Limit:
Here is a test script to test your browser:
Firefox 2: 50 (can bet set between 0 and 65535 in network. cookie. maxPerHost)
Firefox 3: 50 (can bet set between 0 and 65535 in network. cookie. maxPerHost)
Internet Explorer 7: 50 (after applying a patch from Microsoft)
Opera 9: 30
Safari: No Limit(!)
Maximum Cookie Limit:
Firefox 2: 1000 (can bet set between 0 and 65535 in network. cookie. maxNumber)
Firefox 3: 1000 (can bet set between 0 and 65535 in network. cookie. maxNumber)
Internet Explorer: unknown
I'd say that I'm a heavy Internet user but I never scratched those limits. Did you experience problems with cookie limits before?
Update: The cookie limit appears to have been changed in newer browser versions. Newer versions of the Firefox web browser for instance support up to 150 cookies per domain while Google Chrome appears to have a 163 cookies per domain limit instead.
The Internet Explorer cookie limit per host has not changed in newer versions of the browser, it is still set to 50 cookies.