I've never been in a SAR situation. But as far as knives go, I've had my Swiss Army pocket knife for the past 20 years and it is defniitely an item I never leave home without. While it would be a HUGE stretch to say that knife has saved my life on many occasions, I can confidently say that the knife has paid for itself easily.
My dad gave me a nice sheath knife for my 15th birthday. The knife is beautiful, good and sharp. But I never take it with me on any hikes. Why? It gets in the way, hanging off my belt. My Swiss Army knife on the other hand folds up nicely in its puch and I never have to worry about it.