Passenger, a.k.a. mod_rails or mod_rack, is the most common way to deploy Rails (and other Ruby web framework) applications nowadays. It works on both Apache and nginx. It's reliable, good with memory, and runs like a champ. It's easy to install on your own Apache-powered server, of course, but some shared hosts run it too, such as Dreamhost. An older technique is to use fcgi/FastCGI. Most hosts are moving to Passenger, but it's still possible to deploy apps via FastCGI and on some setups it works just great.
Author of Beginning Ruby (Apress): http://bit.ly/t31ag Editor of Ruby Inside and RubyFlow