Can nginx be used as a reverse proxy for a backend websocket server?

You can't use nginx for this currently^{[it's not true anymore]}, but I would suggest looking at HAProxy. I have used it for exactly this purpose.

The trick is to set long timeouts so that the socket connections are not closed. Something like:

timeout client  86400000 # In the frontend
timeout server  86400000 # In the backend

If you want to serve say a rails and cramp application on the same port you can use ACL rules to detect a websocket connection and use a different backend. So your haproxy frontend config would look something like

frontend all 0.0.0.0:80
  timeout client    86400000
  default_backend   rails_backend
  acl websocket hdr(Upgrade)    -i WebSocket
  use_backend   cramp_backend   if websocket

For completeness the backend would look like

backend cramp_backend
  timeout server  86400000
  server cramp1 localhost:8090 maxconn 200 check

How about use my nginx_tcp_proxy_module module?

This module is designed for general TCP proxy with Nginx. I think it's also suitable for websocket. And I just add tcp_ssl_module in the development branch.

nginx (>= 1.3.13) now supports reverse proxying websockets.

# the upstream server doesn't need a prefix! 
# no need for wss:// or http:// because nginx will upgrade to http1.1 in the config below
upstream app_server {
    server localhost:3000;
}

server {
    # ...

    location / {
        proxy_pass http://app_server;
        proxy_http_version 1.1;
        proxy_set_header Upgrade $http_upgrade;
        proxy_set_header Connection "upgrade";
        proxy_set_header Host $host;

        proxy_set_header X-Real-IP $remote_addr;
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;

        proxy_redirect off;
    }
}

Out of the box (i.e. official sources) Nginx can establish only HTTP 1.0 connections to an upstream (=backend), which means no keepalive is possibe: Nginx will select an upstream server, open connection to it, proxy, cache (if you want) and close the connection. That's it.

This is the fundamental reason frameworks requiring persistent connections to the backend would not work through Nginx (no HTTP/1.1 = no keepalive and no websockets I guess). Despite having this disadvantage there is an evident benefit: Nginx can choose out of several upstreams (load balance) and failover to alive one in case some of them failed.

Edit: Nginx supports HTTP 1.1 to backends & keepalive since version 1.1.4. "fastcgi" and "proxy" upstreams are supported. Here it is the docs

For anyone that wondering about the same problem, nginx now officially supports HTTP 1.1 upstream. See nginx documentation for "keepalive" and "proxy_http_version 1.1".