How to quickly check your mining speed?
Very good question. Today I created a page at my pool for this purpose: http://bitminter.com/test

You don't get paid without registering and entering a name and password. But it is useful for the purposes you stated in the question. Just click the "test start" button. You need Java installed, and of course GPU drivers with OpenCL support if that's what you want to test.

PS: Thanks for the idea for this.