While I love the look of bittersweet and the memories it calls up, it's important to know that all parts of the plant are poisonous if ingested (so be especially careful around kids and pets ). That said, it was never a problem in my family.
If you've thought about harvesting bittersweet, it is also critical to know to avoid the Asian variety (or burn it if you have and want to dispose of it). This harmful invasive variety chokes out other plant life; learn more from the USDA. If you still want the look, you can go to a responsible florist or buy artificial bittersweet from a craft store.
Images: 1. Garden Mama 2. Martha Stewart 3. Flickr user Postscript Love via Apartment Therapy 4. Faith Durand for Apartment Therapy 5. A plant similar to bittersweet on Saidos da Concha 6. Studio Choo via Pink Street Design 7. Better Homes and Gardens