Mainly rejection and infection. All the ear ones I have taken out over the years have been due to infection. My immune system isn't very good most of the time so any piercings that I have managed to keep is sheer luck.
My original four nipple piercings rejected so I had to take those out (very painfully and slowly!). I then had the left one done again a few months later but got bored with it because the end result I wanted was the four so I had two in each making a +...and it would taken time (6+months healing per nipple) and a lot of money.
My wrist piercing...well the piercer was at fault for that. He used a bar that was far too short for the amount of flesh he pierced it through...so it was extremely painful and got infected pretty much immediately. I had to take it out after five days.
Had to take my second tongue piercing out because it was through a nerve and I had horrible pains from the back of my tongue all the way down my neck. Then had to take my original tongue piercing out several months later because I got a severe bout of septic tonsilitis and my tongue got extremely swollen and no matter what size bar I put in it felt horrible. So I took it out for a day but then I couldn't get anything back in.
There are so many piercings that I want...but I am so very limited because of my job.