FarmVille Community Manager Lexi has informed the players of this problem at Official Zynga's FarmVille Forums. Some gifting issues have also started and you may find it difficult to accept gifts during this time.
Currently Facebook is experiencing some widespread technical issues are preventing players from accessing various game applications, including FarmVille. We are currently working with Facebook to alleviate this problem as soon as possible, but in the meantime, please be aware that you can still get to FarmVille via our Farmville.com address.
We'll be updating you with more information as soon as it becomes available to us, but for now, please visit www.farmville.com to access FarmVille. We apologize for any inconvenience caused and thank you profusely for your patience with us.
Update: In addition to accessibility issues with Facebook, we are also currently experiencing some technical problem with accepting gifts. With our current problems, there is an extremely high possibility that any gift accepted right now will be lost. Until our technical issues are resolved, we strongly recommend that you do not accept any gifts at this time. When it's safe to accept gifts again, we'll be sure to let you know.
Also, in light of our current issues, Unwither has been activated for all Farmers to make sure that none of your crops are lost if you are unable to access FarmVille at this time.