When you want to sign a PDF, go to the page where you need to add your signature, click the Annotate button on the toolbar (if the Edit toolbar is not visible), and then click the Signature pop-up (which looks like an S with a line underneath) in the Edit toolbar. Choose your signature. (To see this procedure in action, check out this video by Dan Frakes.)
One tip: Write your signature very large, with a marker or a very dark pen, so that it shows up better. When Preview shrinks the signature, it will still display correctly. If you use a standard ballpoint pen, the resulting signature may be too light.
Fill out and create PDF forms
If you've received applications or other documents in PDF, you've most likely encountered PDF forms, which allow you to type right into the fields and then print out (or send) a neat and legible copy. To fill out a PDF form, just click on any of its lines, and type. Preview notices small squares and treats them as checkboxes; simply click in one to check it.
In the past, creating a PDF form was possible only with expensive software such as Adobe Acrobat. Now, however, you can create a form in any text program, such as Microsoft Word or Apple Pages, and anyone with Mountain Lion's Preview can fill it out. You can't share these forms with people who don't use Preview on Mountain Lion; such forms don't work with Acrobat Reader, for instance.
Here's an example: I made the document here with Pages, using text objects to create the small squares and large rectangle, and underlining to make the lines.
Keep PDFs accessible in the cloud
Finally, Mountain Lion brings iCloud storage to a number of applications, including Preview. If you open a PDF in Preview and want to save it to the cloud, choose File -> Move To, and then, from the Where menu, choose iCloud. You'll have access to this PDF on other Macs that share the same iCloud account, but unfortunately you won't be able to view it on an iOS device.
With all of these features, getting to know Preview a bit better is worth the effort. It's a powerful tool, not just for viewing PDFs and graphics but also for editing and annotating PDFs.