(Also posted on LibraryThing)
Here is one big, important part that authors have to remember about posting material for crique: If you are still pursuing a traditional publication path, do no put your stories up on open sites. This is considered using the first publication rights by many mainstream magazine and book publishers.
If the stories are not open to just anyone who happens along -- in other words, you have to register and sign in, then you are (usually) fine. The work has not been presented to the general public. This is true also of posting on blogs, etc. Any time you put your work up where the general public can read it, you run the risk of later facing the first publication rights problem. For people following an Indie Author path, this isn't a problem. Indie authors don't have to run their work past groups of people looking for reasons they shouldn't publish it.
On the site I own (Forward Motion for Writers ) we have a second level of sign in for the private critique groups. This means you not only have to be a member for Forward Motion, but you also have to ask for a secondary access to the private groups.
How helpful are they? It entirely depends on the people involved and what you are looking for. Sometimes it helps to specifically say "I want to know if X works" so that the critiquer is on the lookout for that problem. People getting critiques need to be aware that just because someone gives you a crit of the work that doesn't mean they really know what they're doing. Always beware of the single critique who tells you to make drastic changes. In those cases, be sure you get a second and third opinion, and even then weigh the changes against what it is you want from the story.
When writers give critiques of other writers, they run the risk of drifting into 'I would have told the story this way' reviews without even fully realizing what they are doing. These can be the most difficult ones because they are reworking your story to match what they want.
You are generally pretty safe with grammar and spelling corrections, though this brings up yet another problem. Never post a first draft to be critiqued. Always go through and make all the corrections you can find first. Let it sit for a few days (at the very least) before you look the story over. I know you're anxious to share the wonderfulness of your writing, but posting uncorrected first drafts makes you look like an idiot when people find simple things you could have corrected yourself. You are also running a risk of turning away potential later critiquers and even possible fans. Remember that people are going to talk about your work, for good or bad, to others. Do your best to present a good manuscript, even when you are asking for help.