Can my recommendation letters be repeated? For example, if I am going to apply to 3 REU programs that ask me for 2 recommendation letters each one. 

Can my 2 professors who I asked the recommendation letters send the exact same letters to the 3 REU programs?
Yes, they can.  Sometimes letter writers make minor changes to the letters, for example to add information specific to a given program, but this sort of fine tuning is optional (and almost nobody makes major changes).  The default is to send the same letter.