My wife and I are on cable Broadband 100, which means we get approximately 100 megabits-per-second download speeds. 100mbps is currently the fastest modern-day connection that you can get for wired home service in North America. While most of you don't need 100mbps, you should be getting at least 8 megabits per second to consider yourself a modern user. Anything less than 8 mbps is slow.
Here is a visually-pleasing way to test your internet connection speed. Speedtest.net is a Flash-Javascript tool by the people who made Ookla. Use this free tool to measure your internet service provider.