I just move my experience on C# into Ruby. Ruby is very interesting programming language, I really like it. I do know Rails is a web application framework that are used by lots of web developers and uses Ruby language. What else of applications should we build on ruby?
The types of applications that Ruby seems to excel at are designing frameworks implementing a DSL. The loose structure of the Ruby syntax and reflective/meta-programming style encourages redefining structures with out necessarily having to implement a parser of your own. Things like Rake, Rails, Sinatra, Capistrano and RSpec all have a very particular DSL that is quite expandable by adding the full power of the Ruby language within the DSL. Of course, one of the biggest strong suites of Ruby is fast development, especially in convention-over-configuration frameworks like Rails. Obviously, data-base driven, dynamic web applications have a strong foot hold in Rails, but there is nothing stopping you from building the next rails of SMTP.
Ruby excels at driving highly configurable applications, where the configuration can be programming itself. I know I saw Zed Saw talk about writing business rules style Access Control Lists in Ruby to allow a more dynamic reaction to changing laws and rules. Ruby Arduino Development could also help change the face of custom robotics and physical computing by putting a powerful and easy to use scripting framework for interfacing with the Arduino physical computing platform (a "Make"rs dream).
You have probably noticed a theme of agility in software, which is exactly where Ruby belongs.
Update, desktop applications: There doesn't seem to be any killer desktop applications for Ruby at the moment, mostly because there is such a demand for web applications and providing rich application experiences via the web is getting easier and easier. There are frameworks for Ruby GUIs though. Of particular note is Shoes written by _why the lucky stiff (a Ruby rockstar) because it presents GUI development in an especially Ruby way. Other than shoes, lately Macruby with native Cocoa support has garnered some attention. Then you have GUI toolkits with Ruby wrappers: WxRuby, FXRuby and Ruby-GNOME2.
Just because there are no killer apps for Ruby GUIs right now doesn't mean you can't create the next one.
I think Ruby is suitable to write small software tools we use every day to improve our productivity.
Download an XML export of Wikipedia, and analyse it in some novel way.