I'm a recent whovian who was first introduced to Matt's Doctor, which quickly became my favorite. I didn't feel Nine's regeneration was sad, because he didn't seem too sad about it. And Ten's regeneration, I kinda felt for him, but at the same time I was excited that we were going to move on to Eleven. I will most definitely be sad to see Eleven go sometime in the future.
Truth be told I've so far been more sad about companions leaving than the Doctor having to regenerate. Donna's departure was uber-sad for me, same with the Ponds (Donna and Amy were my favorite companions). Rose's departure was sad, too, but I kinda got a bit caught up with the awful translation of "Bad Wolf Bay", lol ("Dårlig Ulv Stranden" is an awful attempt at making up a fictive Norwegian place name - we simply do not name places that way, also "Dårlig" means bad in terms of not being good enough, feeling ill or food items being past their expiration date, I think they'd be better off using "Farlig" (Dangerous) or "Slem" (Bad in terms of not being nice) - and "Stranden" means "the beach", our word for "Bay" is "Bukt"). Martha's departure was kinda an empowering one for the character, someone choosing to go because what the Doctor is willing to offer her is not enough for her.