I have no insurance and currently cannot afford private insurance...
I pay for my weekly therapy session on a sliding scale through the county I live in ($27.00) which is Johnson County, KS. The county offers free crisis care and and almost free inpatient type of Crisis Care center where you can stay for a couple of weeks if you are either suicidal or going through a some sort of truma, it's NOT a hospital though, but an alternative.
The county does offer hospitalization if needed as well and you pay according to your income, the rest is coverered by gov't subsidies and grants.
There are many different free groups in KC metro area too (group therapy) for just about every psychiatric issue.