When it comes to remote access, we enjoy LogMeIn, but its $31 price can be a bit off-putting. However, with a recently released new version of the app, you can get basic remote access for free.
The new version of the app allows you to access files on your home computer, control and run programs on your Mac or PC, and edit files. If you need more features, there's in-app purchases to get access to video, remote printing, photo management, and a few other options (though at $39.99, these are actually slightly more expensive than before).
You will, of course, also need to snag the free program on your computer at home, but as a completely free way to control minor things on your PC or Mac, its works well. If you already plopped down the $31 in the past for the extra features, you get grandfathered into everything included in the in-app purchase. It's a free download for iPad and iPhone in the iTunes App Store.
LogMeIn [iTunes App Store]