I have to develop an app which has to works on every kind of device like desktop, iPad and mobiles. This app will not use any native UI. The only thing is it has to be developed using Force.com. Any idea which framework (like Bootstrap) fits well while working on Force.com?
The easiest and simplest starting point is to look at the hybrid samples in the force.com Mobile SDK. By default, these use jQuery Mobile which takes care of optimising the app UI for various screen sizes (to a certain extent). You can always replace jQuery Mobile with any other HTML5 framework such as Sencha Touch, Twitter Bootstrap or any other. The above holds true if you want to develop apps which install on devices.
On the other hand, if you simply want your VisualForce pages to be rendered optimally across multiple devices, you should strongly consider looking at Mobile Components for VisualForce - http://wiki.developerforce.com/page/Creating_a_Mobile_Component_for_Visualforce
If you want to use jQuery Mobile in VisualForce pages, please take a look at this tutorial - http://blogs.developerforce.com/developer-relations/2011/07/jquery-mobile-in-visualforce-pages.html
If you want to use Twitter Bootstrap, this is a good starting point - http://blog.tquila.com/2012/10/22/using-twitter-bootstrap-with-vf-pages/
Hope this helps.