On Writing Stack Exchange
While critiques are off-topic on the main site, they are welcome in chat (Beta Reviewers/Reviewing) for those who have 20 reputation.
Online critique sites
Fictionpress 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. It's easy to use and has a large user-base. source
Critters Workshop is an online critique group. (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. It used to be science-fiction/fantasy/horror only; those parts of the site have been around longer than the the other genre sections. source, source
Critique Circle is members-only: Work put up for critique isn't visible unless you're a member, so it's not "published online". source
Sites with a critique section:
Scribophile has tools for helping with structuring critiques that are quite helpful. You earn points to make submissions depending on the length of critiques and whether they are appreciated by other site members. Critiques are visible only to members. source May have a heavy focus on scifi.
The Erotica Readers and Writers Association. They host a "Storytime" mailing list where you can post your work for critique. source
r/writing has a weekly critique thread.
r/scifiwriting allows general critiques. It's a small subreddit but looks pretty active.
r/DestructiveReaders encourages brutal critiques.