Yes. For example, m.twitter.com is Twitter's mobile site and should show up just fine on a computer. To get to a site's mobile version on a computer you have to know what it is first. Going to twitter.com will take you to twitter's regular computer site on a regular computer, but automatically redirects you to the mobile version when you go there on a mobile device. You can always do a search for the mobile version of whatever site you are interested in looking at, or if you'd like to be automatically redirected to the mobile version you can try spoofing your browser's user agent to mimic a mobile device. To do this in Firefox you can get an extension like this one: addons.mozilla.org
Sometimes going to a mobile version will set a cookie so that even if you type in the nonmobile version you will see the mobile version anyway. Deleting your browser cookies will fix this.
Sometimes going to a mobile version will set a cookie so that even if you type in the nonmobile version you will see the mobile version anyway. Deleting your browser cookies will fix this.