(For current known solutions to this problem, see the Updates below! Thanks for visiting and making this my most popular post ever, even over a year later!)
If you’re running Outlook 2007, you’ve likely noticed that you can’t preview Ryan Gregg , someone who works on the Outlook team at Microsoft, has released an add-in on his blog  to let you preview those PDFs! It uses Adobe’s Reader ActiveX control, so it’s genuine Adobe doing the previewing. I’ve installed this and it seems to work well; I get quotes from our primary supplier as PDF attachments all the time and this will come in very handy indeed. I installed the add-in while Outlook 2007 was still running and was able to preview a PDF attachment as soon as the install completed, no restarts. YMMV.
Update in August 2007: Adobe Reader 8.1 has PDF Previewing  built-in, so Ryan Gregg has pulled the add-in down off his site.
Update in April 2008: This post is still very popular, so here’s an update: If you don’t want to install Adobe Reader 8.1 to get Outlook 2007 Foxit PDF Preview Handler  which uses the very lightweight and fast Foxit Reader software  to preview PDFs in Outlook 2007. The original version  is for Office on Windows Vista only, but last month the author wrote a Foxit Preview version for Windows XP  as well! I use the Foxit Previewer myself as well as the full Foxit Reader for reading writeup and pointer to the Foxit Previewer , I may have gotten my original link to it from him (not sure right now).