Is it common for patients to fall in love with their doctor or therapist?

Not uncommon. After all, it's nice to have a caring thoughtful person listen to your every word. But clients usually don't know very much about their therapists personally, and so are "in love" in their imagination mainly. Also, therapists are trained & duty-bound not to reciprocate — to maintain professional boundaries. Best to discuss your feelings with your therapist, & use it to learn about yourself.
Pretty often. At least temporarily, patients may feel they're in love with their therapists. These feelings can be intense -- & often come from transferring feelings towards important others from early life, onto the therapist. Being truly heard can arouse deep feelings too. These patterns generally mirror the person's issues with others in daily life; discussing & working through them is part of therapy.