When I adopted Bailey, back in 1995, I didn't know anything about greyhounds, and to be honest I wasn't given much information when I adopted her. I used to take her hiking off leash daily. She was really good. She would often stop and look back to see where I was and really never got very far ahead of me. She never approached other people or dogs...she just wanted to do her own sniffing and moseying along. However, she did and would take off after rabbits, sometimes running completely out of my sight, which would freak me out. There would be no stopping her once she spotted something...she wouldn't even know who I was any more. And she didn't come back for me...basically, she would wait for me to catch up to her. I will also tell you that she injured herself quite a few times. Sore wrists, cuts, scrapes, punctures...lots of vet visits. I look back at pictures of her and she often has vet wrap on her somewhere. After finding greytalk, I realized that she wasn't supposed to be off leash. I felt like I really couldn't change at that point. She'd had so much freedom for a very long time...it would be like making an outdoor cat an indoor cat. Anyway, Bailey loved her life. She had some amazing times and there were quite a few heart attacks for me.
When I got Holly, I never let her off leash. The biggest difference was vet bills. Holly never got hurt. Never needed the vet except for yearly exams/dentals. She also was a very happy dog. She wanted her two walks a day and was perfectly content with that.
Now, I have a lab. She gets to go off leash once in a while, when hiking. She is crazy and zooms all over the place. I don't think she realizes that there is even a path. She chases rabbits way the heck out in the brush. The difference is that she has nice, thick skin and has had no injuries. She is a sturdy girl. I also have a GPS collar on her in case she gets too carried away. I am also thinking about getting her a rattlesnake vaccine.
I will never let another greyhound off leash in a non-fenced area...except perhaps a secluded beach.