For us this was fixed by editing the DOCICON.xml file located here on your WFE server: C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\14\TEMPLATE\XML

You need to Change the value for PDFs. Our value was originally set to this: Mapping Key="pdf" Value="pdficon_small.png" OpenControl="AdobeAcrobat.OpenDocuments"/

We modified the OpenControl to "" so it reads like this: Mapping Key="pdf" Value="pdficon_small.png" OpenControl=""/

Then do an IIS reset. Now the PDFs open directly into your browser without prompting you!

For us this was fixed by editing the DOCICON.xml file located here on your WFE server:

C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\14\TEMPLATE\XML 

You need to Change the value for PDFs. Our value was originally set to this:

Mapping Key="pdf" Value="pdficon_small.png" OpenControl="AdobeAcrobat.OpenDocuments"/

We modified the OpenControl to "" so it reads like this:

Mapping Key="pdf" Value="pdficon_small.png" OpenControl=""/

Then do an IIS reset. Now the PDFs open directly into your browser without prompting you!