My last ultrasound was done at 19 weeks and my ob/gyn said I don't need another one unless there is a medical reason that they would need to see the baby. Is this correct? Is the last ultrasound typically done at 18 weeks?

Depends on the doctor, but after that they're just making sure that everything is growing as most the development is done. If you're doctor is satisfied that your child is progressing fine than you shouldn't worry either.