I'm an active guy, I work with my hands and engage in a number of extreme sports, not to mention I play basketball...and anyone that plays basketball knows the sport is the king of jammed fingers and damaged digits. After a few quick calls to the local hospitals, I quickly discovered the amputation risk is a myth, and many if not most hospitals have the tools to remove titanium, along with rings of any other metals - gold, platinum, cobalt, etc.
Now that said, the one downside with titanium is once your ring is cut off, there's no putting it back together again. It's like Humpty Dumpty, but in a cool space-age material. Gold and most other precious metals can be melted down and recast, but with titanium, you'll need to buy a new ring. That said, we've got you covered at Støberi...anyone that goes through a medical procedure where they have cut off their Støberi ring shouldn't have insult added to injury and then have to buy a replacement ring. We'll cover the costs...as long as you'll let us post some gnarly photos of that injury of your's in our Men's Guide.
This particular rumor is so pervasive, the good people at the myth busting website Snopes.com have an entire article on it. (Scroll down in their article to learn about a verrrrry sensitive titanium thumb ring that was removed. Absolutely unimaginable...but if that ring could be removed safely, I think your ring finger is a comparatively easy job.)
All kidding aside, there really isn't any health risks by purchasing titanium jewelry. In fact, the hypoallergenic nature of the metal makes titanium a great, safe option. In general, stick to 100% pure commercial grade - the exact type we use at Støberi - as it's a bit easier to remove. Also, please use some common sense. When playing sports, and particularly basketball, take your ring off and put it somewhere safe. No point damaging a perfectly good Støberi ring just so the boys at the lunchtime pickup game know you're a taken man.