If you are not willing to pay for any app which you need then you can use a Cydia app called Installous. Before installing and downloading paid apps for free you have to understand that this is unethical and to a certain level illegal also because the server providing free paid apps is violating the copyright law. I am only mentioning the software here for learning purposes so that if someone still wants to download paid apps for free he can use this software.
How to install Installous on iOS 5.1 iPad, iPhone or iPod Touch
Note: To install Installous Cydia App you need to jailbreak your iphone, iPod or iPad, click here to go to the tutorila on How to jailbreak iOs 5.1 and iOS 5.0.1.
You can follow my guide on How to add sources to Cydia and give the source address http://cydia.hackulo.us when asked and install as mentioned in that tutorial after adding the source you will find Installous 4 in the sources just tap and install it. Now you can download free paid apps of any value if available at the server.