Beta web application Netalyzr is a free tool that analyses your network for possible problems—large and small—helping you determine your overall network health.
As soon as you start the test (and agree to the security certificate), Netalyzer performs various tests on your computer's connection. When the tests are complete, you'll see an exhaustive rundown of all the results, including a handy "Noteworthy Events" section at the top that details the possible problem areas. Tests that pass are marked as green, minor problems are marked in yellow, and problems get the classic red. For a longer explanation of what each section is testing, just click the linked section title.
Did you give it a go? Let's hear how your network handled the test in the comments.