There are many websites which offer you to earn free Bitcoins. With most of these sites, the concept is that you visit the site and just for looking at it you get a small amount of Bitcoins. The concept has something in common with watching good old free TV. You watch a lot of ads and inbetween you get something you actually want to see, like a film or music clips.
While this is a legitimate concept, the return on your invested time is very little. So when you earn Bitcoins from these advertising sites, the Bitcoins actually come at the cost of your time. As the saying goes 'there is no free lunch'. But see for yourself, here is a list of some of the sites that I find interesting
BitVisitor :: Earn Bitcoins for watching websites or videos. Every page is shown for five minutes. Then you can click 'Next' for confirmation and move on to the next page. What I like about this site is that payouts come within roughly an hour. This is a major advantage compared to other sites that pay Bitcoins for completing tasks. Also, you don't need an user account here, you just enter your Bitcoin address. The amount of Bitcoins you can earn here is limited though. Per five minutes you get something like µBTC 100 (that's 100 microcoins or BTC 0.00001) which means that your hourly payout is something like BTC 0.00012. That's not too much money but it is a start to make you first Satoshis and get familiar with Bitcoin. And note, payout per five minute period varies. So the above calculation only holds if the average payout per five minutes is µBTC 100.
freedigitalmoney.com :: Earn Bitcoins by getting rewards fo purchases made in Bitcoin. On this site you also don't need a user account and just have to enter your Bitcoin address to earn Bitcoins.
CoinWorker :: Earn Bitcoins by completing analytical tasks. A user account is required here. I haven't tried this service but payouts seem to be a bit higher than with the aforementioned sites.
Bitfortip :: Earn Bitcoins by answering forum questions. This is a nice service because it brings people together who are interested in Bitcoin and many other topics. At the same time it allows to pay rewards in bitcoin for answering questions. This is something that would not have been possible without a currency like Bitcoin that has low transaction fees and instant transfers
Earning Bitcoins from completing tasks on websites is a viable option to actually earn some Bitcoins, but don't expect your income to be very large. I regard it as a first step to get familiar with Bitcoin in general. Also, it is interesting to see what kind of services are enabled through frictionless money transfers.