There has been some good answers to your question already but I thought I would throw my view in as a user of many web apps, some paid for and some free.
My favourite SaaS or web app model is offering a fully featured free trial for 30 days (or whatever timescale is most relevant) and then dropping down to a free version at the end of the 30 days if the user does not start paying.
So that would not involve entering credit card details until you are ready to actually start paying for the product.
I am a user of TactileCRM, currently using the free version after having use of the full version for 30 days. Once my business is ready for it (very nearly now) I will definitely be subscribing to the paid version because I know I will use the features the paid version gives me.
I am also a user of Freshbooks and also used their free version until I had enough clients that warranted paying for their excellent product. I am so keen on Freshbooks that I actively look for other apps that work well with Freshbooks.
Finally, I am also an avid user of Evernote and use it every day. I use the free product and do not envisage needing the paid version for the foreseeable future, as the free version suits my needs very well.
Those are just a few examples of web apps that I currently use and am a big fan of.
Notice that even though I am not a paying customer of Evernote (or TactileCRM yet) that I still support the product and tell people how great it is (please see other answers that I have submitted to this site for evidence and my Twitter stream @TomBatey).
I know that offering a 30 day free trial and then dropping down to a free version with fewer features after 30 days is not suitable for every SaaS product but I find it my preferred model when considering signing up to an app.
Hope that helps.