Fictionpress is a popular website that allows anyone to upload stories, read those stories, and comment. As the site is wide open, the quality of comments varies wildly, along with the quality of stories. Earlier in my life, I frequented the site, but I eventually left, as I wanted more constructive feedback than I tended to get there. It does have the advantage of being easy to use and having a large user-base.
A quick google search indicates there are also a number of clones. I cannot comment as to their quality, having never tried them.
If you're looking for more critique and less friendly chit-chat, as I was, I would recommend joining an online critique group like Critters. Critters is designed to encourage participation (you have to give about 3 critiques per month to have your stories critiqued). It is also designed to encourage useful, constructive, and in-depth feedback. I typically get 10-20 critiques on any story submitted, with 90% or more being very useful. The science-fiction/fantasy/horror portion of the site has been around for some time, but the other genre sections are new, so I don't know how populated they are at this point in time.
Also, be aware that making a story freely available to anyone on a site like Fictionpress effectively uses your First Electronic Rights, and possibly others. This means you are no longer able to sell those rights. This can be a big turn-off to publishers. You may want to do some research on publishing rights before putting a story online, if you plan to submit it for publication.