What would be a proper way to simulate a large number of requests to test if my web application can handle it?
You could try using Microsoft's WCAT tools. Look here: http://support.microsoft.com/kb/231282
They're free, too. That's always nice.
I've used JMeter in the past, and I find it to be very useful for stress/load testing as website, even ones written in ASP.NET (with or without MVC).
In general you would want to (with any tool) write a script of what an average user of your site would do. You may even end up creating multiple of these scripts. Tools like JMeter even allow for a random element to be added to a script. With these scripts created a load testing tool can then simulate as many users as you desire hitting your site.
I would recommend allow JMeter to slowly ramp up the number of concurrent users and watch the response time graph. At the point where the response time starts increasing too highly is at the point where you've hit the maximum number of users (given you scripts) that your site can handle.
Depending on your budget, you may be interested in some load testing software designed for this. A Google search brings up all sorts of alternatives. This is probably the best way to do it.
This one has a free trial version and isn't too pricey, but I would recommend shopping around first.
ab and httperf are two, more unixy options, if you don't mind delving in that direction.
There's a nice screencast for using httperf by peepcode.
Post the URL on stackoverflow.
Make it sound like a challenge, so lots of people come check it out: "Can you find the hidden performance problem in this app?"
Use the load testing tools from Visual Studio Team System. 2010 if you can get it.
The tools are great to use and provide wonderful instrumentation. There is also a programming model to go with the tools, allowing you to make some very complex testing scenarios possible.