Speed test sites and software are popular these days. Lots of folks check out download speed tests regularly to see if they are truly getting the speeds they are paying for.
Your results may vary if you run a test more than once on the same connection. This is due to the test measuring how fast a certain amount data can travel across the live Internet and back to your computer. It doesn't measure the theoretical speed (Usually Documented by your ISP) of your connection, but the speed at which your computer receives and transmits data over the Internet.
The different results from tests can be due to internet congestion. Or it could be from varying paths in the 2 speeds or some less efficient tests will use the cached version of the page to test, this is the least accurate method for testing speeds if the systems cache can affect the results.
Should you test your download speed? Well absolutely, if you are paying for a 1 mb connection and you are consistently getting speeds around 300kb then you are not getting the connection you are paying for. This happens quite a bit, especially in rural zones.
Utilizing an online speed test to test your download speed will allow you to monitor your speeds. But don't forget what I said earlier about how the values can differ.
There are several speeds tests available in google, just search for internet speed test to see a few of the top ones.