HAProxy and SSL

HAProxy does not have support for SSL. Common solution is to use Stud to handle SSL and send un-encrypted data to the backends.
Terminating SSL in the load balancer is not considered a good idea because it does not scale.
It is considered better to use webservers like Nginx with session caching enabled.
Good benchmark comparing Nginx, Stud and Stunnel is here- http://vincent.bernat.im/en/blog/2011-ssl-benchmark.html.
Another benchmark comparing stud,stunnel and nginx: http://matt.io/entry/uq and the follow up which establishes Nginx to be just as performant as Stud - the key is picking the right cipher.
http://matt.io/technobabble/hivemind_devops_alert:_nginx_does_not_suck_at_ssl/ur

Tomcat with HAProxy/Nginx

Tomcat is usually fronted with a http server for various reasons - security, load balancing and additional functionality like URL-rewriting. Most common options for the proxy include: HTTPD, HAProxy and NGINx.

Compile HAProxy from source
$ make
$ make TARGET=generic
$ sudo make install

Resources:
http://www.tomcatexpert.com/blog/2010/07/12/trick-my-proxy-front-tomcat-haproxy-instead-apache
http://www.mulesoft.com/tomcat-proxy-configuration
http://haproxy.1wt.eu/download/1.2/doc/architecture.txt

Comet technology

Server Push, long polling, Good descriptions here: http://code.google.com/p/google-web-toolkit-incubator/wiki/ServerPushFAQ
Maturity of Comet implementations: http://cometdaily.com/maturity.html
Best Comet/Streaming server: Caplin Liberator (http://www.caplin.com/caplin_liberator.php)