With the high pressure for physical beauty and our culture's worship of the temporary, this is an important question. Most Christians would probably respond to the question with a strong "Yes!" But even right-intentioned motives need to be tested with God's Word. 

I've heard some believers accuse cosmetic surgery of being vain and probably in most cases it is. But let's consider the logical conclusion of this kind of thinking. Is getting surgery itself a sin? No. Then why is cosmetic surgery sinful? One might reply, "Because altering your appearance is a sign that you are not content with how God made you." Does getting braces for your teeth alter your appearance? Yes. So to be consistent, one has to surrender that getting braces is sinful too. What about wearing contacts? What about coloring one's hair? To make a blanket rule that cosmetic surgery is sinful is legalistic and immature. Although I agree that more often than not, cosmetic surgery and things like it can grow from a heart of vanity, I cannot judge other people's motives. So my convictions too must be tested by God's Word. 

Paul wrote in 1 Corinthians 10:23 "All things are lawful, but not all things are profitable. All things are lawful, but not all things edify." Unless an action is a direct violation of God's law (like murder, lying, or stealing) the action itself is not sinful. Cosmetic surgery fits this category. So instead of throwing a blanket rule over every type of cosmetic surgery (along with dancing, drinking, alcohol, tattoos, and millions of other things), we need to ask the simple question of motive. Why did this man or woman alter their appearance? Was it to serve a temporary want? Or was it ultimately to honor the God who gave us the gifts of our own bodies, orthodontists, makeup artists, surgeons, and medicines?

Most women who lose their breasts through breast cancer have cosmetic surgey to recreate look-alikes. One could argue, "Aha! She was not content with how God allowed this trial to change her body so her action was vain." But what if she was doing that to please her husband? Is that vain or is that simply pure love? Many Christian woman who go to a tanning booth (if you're from California) or a tanner (if you're from Michigan), would condemn plastic surgery while they themselves subject their skin to 93-99% UVA radiation, a level that could produce skin cancer. That's not consistent. In this case I think they'd find it harder to defend artificial tanning than plastic surgery. 

What about piercing one's ears? If one labels cosmetic surgery sinful, she's going to have a hard time giving a good reason why drilling a hole through ones' body isn't sinful too, since after all, one could argue that it's not being content with the way God made you. Even makeup is an alteration of one's appearance. 

So at the end of the day, instead of asking, "What's wrong and what isn't?" on gray areas like these, we should instead be asking, "How can I honor God with my body today? How can I use it to build up Christians and reach the lost for Jesus?" If those are one's driving motives, the believer will know the right thing to do.