This is a very interesting (and it is becoming a more frequent) question! In a word the answer is Yes - however there are many, many variables here!
Answering this question quite literally you could sit in front of your computer, have a webcam and charge people for being able to view you - of course that is not everyone's "cup of tea" Webcam models are making a LOT of money online and I will leave a "tag" link at the bottom of this blog entry so that you can see some of the past posts that I have made concerning webcam models. But then complications arise because how are you going to accept payment? Paypal is very popular but Paypal will not accept transactions of a "sexual" nature. But there are other ways to accept payment simply because there are so many webcam models online who are accepting payments electronically. And like I mentioned before, webcam models are making a lot of money simply by having a webcam and a way to accept payments.
You can take something that interests you and start either a webpage or a blog. However it will take some time before you can raise interest in your site and the sooner you raise interest will depend on how much work you put into building up your site. You can sell a product, sell a service or accept advertising on your site. With the later you site has to have a good reputation before you even start to approach possible advertisers or sponsors. If you have a pagerank "widget" on your site and your pagerank is high you may get advertisers coming to you! (This has happened to some of those that have sites with a high page ranking). If you sign up for and use Google's Adsense program you won't have to go seeking advertisers because they will already be there for you. Here is a link to a blog post about how much some people have been earning with adsense:
However even being a part of adsense requires work and effort on your part. You have to earn at least $100 during the month before you will be issued a payment. If you don't make $100 during one month then your earnings will be rolled over into the next month and so on until you have earned a total of at least $100 - then you will be issued a payment by the end of the next month.
So basically the answer to the question "Can I Sit In Front Of My Computer And Make Money Online?" is Yes - BUT it will require work on your part!