Healing is an important part of any adventurer's life. And thus so is dealing with healers. This provides ample opportunities for roleplaying scenes.
There is the well-known Florence Nightingale effect*, where a caregiver falls in love with the patient, and there is also the inverse case, in which patients fall in love with nurses or doctors. With suitable healers looking after PCs you could develop this into a storyline.
Alas, not all patients can be looked after like Faramir, who was fortunate enough to be nursed back to health by Eowyn. Some get rather less endearing medical aid...
* Interestingly, the Wikipedia article on this effect claims that it was first referred to by that name in the film Back to the Future! We're not entirely sure we believe that, but there you go. EDIT: Now that we've pointed this out, the article has been updated to include an earlier reference, complete with citation. Darths & Droids: making Wikipedia better.
2-1B: Now sir, remember you're not back to full strength. Avoid swimming, pregnancy, operating heavy machinery, carrying loads, mental exertion, eating exotic food, and miscellaneous inverted postures.
Luke: No problem. I'm sure I won't do all those things.
Luke: I assume you're packing the medical facilities.
2-1B: Yes, sir. I have initiated evacuation protocol mu-gamma.
2-1B: Oh wait, that's the pre-colonoscopy procedure.
2-1B: Whoopsie! Better start again.
Luke: Okay, I really need to go now.
2-1B: Oh my. You may also want to regurgitate those tablets I gave you.