How to edit PDF files in Illustrator or Photoshop
If you have the full version of Acrobat (not just the free Reader) and Adobe Illustrator & Photoshop installed on the same computer you can edit any part of a non-protected PDF file.
With your PDF file open, find out where the "Touchup Object Tool" is in Acrobat. It's a black arrow tool, just like the one in Illustrator, and it's usually hidden under an outline of the letter "T" (the touchup text tool) in a little submenu. You might first have to right-click in a blank part of your toolbar area and check the "Editing" toolbar to turn the Editing toolbar on.
Click on the object you want to edit with the arrow tool so that the object gets a black box around it (it is now selected). Right click on that object (control click on the Mac).
Then in the submenu you'll get an option to "edit object" or "edit page", choose that. Illustrator will open automatically with your object or page in a Temp file. You can make a variety of changes to the PDF objects in Illustrator that you can't do in Acrobat.
When you're done editing choose File:Save. Do not choose Save As.... When you do save, the new object is placed right back in the Acrobat PDF file in its new form. You should be able to see your changes right away in the Acrobat window. Don't forget to save the PDF file when you're all done.
Note: Compare your new page with the original to make sure things like Check boxes haven't disappeared in the conversion. Some fonts can cause problems. Also, you sometimes have to select a bunch of objects in Acrobat because the file consists of many of separate objects. In this case, choose the black arrow tool and then do Control-A (select All).
Then right-click on one of them and choose Edit Object, like above.
Finally, you can edit scanned graphics in a PDF (i.e. a TIFF file) the same way, it just opens an image editing program like Adobe Photoshop instead of Illustrator when you choose "Edit Image...". You might have to tell Acrobat where Photoshop.exe is under File:Preferences:Touchup. Thanks to PlanetPDF for documenting this feature.