Macworld explains how to run iPad or iPhone apps on a Mac OS X or Windows laptop or PC - or at least simulate them. (Updated, 8th May 2014)
Apple controls the way you use the software you download from its App Store quite tightly, and it's very difficult to run your iPad and iPhone apps on another platform, such as your desktop Mac or MacBook or even a Windows PC or laptop. Probably the best solution is to download simulator software that mimics the behaviour of an iPad on a different platform. (We originally called this emulator software but readers astutely pointed out that simulator is the correct term for what iPadian does.)
The best iPad simulator for Mac and PC that we've found is called iPadian, which you can download from PCA Downloads. (We've heard reports of some security software flagging the download up as possible malware, but that's a safe source and there's no need to worry.) iPadian, which is based on Adobe AIR, creates an iPad-style interface in a window on your PC or Mac desktop and runs the apps (or close approximations of them) within that. It looks terrific - the apps look almost exactly the way they would on an iPad or iPhone - and installation is straightforward.
But bear in mind that this isn't a method that allows you to transfer your existing library of apps to the Mac or PC. You have to select and download apps from iPadian's own app store, which obviously can't offer anything like the same range of options, but there's still a decent selection, and many of them are free.
We'd also warn that playing touchscreen-optimised software on a mouse-and-keyboard or touchpad setup isn't ideal; even though the simulated interface is well recreated, you may find the apps harder to use than they would have been on their intended original platform. As Mike Williams advises on PCA, the program doesn't allow you to use the mouse to simulate swipes, but spinning the mouse wheel will scroll occasionally.