Picasa 3.9 finally has great integration with Google+, allowing you to easily upload and share photos on the service and tag friends. Even if you don't use Google+, you might want to download the update for new editing features.
There are 24 new photo editing effects in Picasa, as well as a side-by-side mode so you can compare photos (useful when photo editing).
The biggest new update is the Google+ integration. There's a "Share on Google+" green button now at the bottom of the program, which leads to a form for sharing the photo and adding to a Google+ album. The tagging feature is pretty useful too. According to the Google Photos Blog:
Tag people in your circles: When you click a photo to tag a friend, the dropdown menu now includes people in your Google+ circles in addition to your Gmail contacts. If you tag friends from Google+, Picasa will automatically suggest that you share your pictures with them when you upload your album.