Americans had more babies in 1987 than in any year in nearly a quarter-century, but at the same time the nation recorded more deaths than any year in history, according to figures compiled by the government's National Center for Health Statistics. A slight increase in fertility, coupled with the huge number of women in their prime childbearing years, resulted in an estimated 3,829,000 new arrivals last year, the most since 1964, the center reported in its preliminary statistical summary for 1987. Millions of people born in the post-World War II Baby Boom are now in their 20s and 30s and, after completing school and launching careers, have begun families. Births in 1987 were up from 3,731,000 a year earlier. Deaths in 1987 totaled 2,127,000, up from 2,099,000 a year earlier and the most ever recorded for a single year in the United States.