Do babies conceived naturally or artificially have any differences in long-term health?
A review paper on children born by the advent of assisted reproductive technologies (ART) and frozen sperm (Lansac &amp; Royere, 2001) concludes that ART children, as compared to the general population:


Have normal weight;
Do not suffer increased occurrence of premature births;
Do not have increased rates in stillbirths;
Have equivalent sex ratios;
Show no increased occurence of birth defects and no chromosomal abnormalities;
Have normal overall health.
Have normal psychosocial development, at least up to 8-9 years of age, but the available data is scant in this area. 
However, the rate of multiple pregnancies was higher in the ART group. This may be caused by excessive hormonal treatments during artificial insemination therapy, or by ovulation induction treatments and embryo transfer policies (multiple embryos implanted) that may increase the rate of multiple pregnancies.


The authors do conclude that larger and longer studies are needed to support these findings more conclusively, given that their review paper was based on just two studies. It deserves note, however, that both of these studies were prospective in design and included a large population of subjects.  

Reference
- Lansac &amp; Royere, Hum Reprod Update (2001); 7(1): 33-7