While this card certainly isn't universally good, there are a few situations where this card can certainly come in handy. Titanium Ribs is certainly the bee's knees vs PE, especially when comboed with I've Had Worse or Synthetic Blood. Titanium Ribs + I've Had Worse can literally save your life against Scorched Earth when they try to use Traffic Accident to dodge the IHW. These are, of course, fringe cases, and a card that's only marginally useful against a handful of identities normally isn't worth the card slot. Where TR really shines is in self damaging decks.
The most obvious combo is Amped Up and Wanton Destruction, giving you five clicks to burn the Corp's entire hand, with no chance of discarding the all-too-important Destruction. The best time to use it is when you KNOW you'll be damaging yourself often. Enter Stim Dealer. Many people don't know/realize that Stim Dealer is NOT unique, thus allowing you to gain a whole lot of clicks , and only suffer the brain damage every third turn. Since you know you'll be taking damage often, Titanium Ribs (along with some kind of hand-size increase like Cyborg Skull, Health Insurance, Japanese Paper Airplanes, or A Nice Suntan) will mitigate the consequences of this repeated damage.
It certainly isn't a card for every deck, but don't count out Gabe's Freaky Wolverine Skeleton entirely.