My Grandmother moved to Delray Beach many years ago and has had a long history of good experiences and no crimes.
That said a great resource to determine crime rates is to call the local police station or visit their web site:
In the case of Delray Beach take a look at: http://www.mydelraybeach.com/Delray/Departments/Police/Activ
browse around-- the police blotter is even online so you can see the most recent calls!
Of course you may find that the best analysis is through a comparison of where you live now.
The short answer is absolutely. Like any town in South Florida - or anywhere else for that matter, whether it be Boyton Beach, Delray or Coral Springs, you should check different neighborhoods of the town to see where you feel the most at home for your retirement. Delray has a beautiful downtown area, quaint shops, family owned restaurants and terrific entertainment. It is as safe as any other South FL town, and to find an area around there to live, I would ask the local Realtor to email you some homes in your price range. The homes further west of downtown should be newer than the ones closer to the coastline due to the natural expansion of that area.
Let me know if I can help you further.
Best of Luck,
The Realtor Referral Assistant