According the the Centers for Disease Control's National Vital Statistics Report Births: Final Data for 2006:

In 2006, 143,625 live multiple birth babies were born in the United States:

"The upsurge in multiple births, particularly higher order multiples, has been attributed to older age at childbearing (women in their thirties are more likely than younger women to conceive multiples spontaneously) and the growing availability and use of fertility-enhancing therapies (both assisted reproductive technologies (ART) such as in vitro fertilization), and non-ART therapies such as ovulation-inducing drugs and artificial insemination.

Less than 20 percent of all triplets/+ born between 1997–2003 are estimated to have been naturally conceived. In response to the unparalleled rise in higher order multiple births and their attendant risk of poor outcome, the American Society of Reproductive Medicine published guidelines in the late 1990s (later updated), intended to reduce the incidence of triplets/+ resulting from ART by limiting the number of embryos transferred. Studies have since documented substantial declines in such transfers." (Source #4)

Sources:

1. United States Department of Health and Human Services (US DHHS), Centers for Disease Control and Prevention (CDC), National Center for Health Statistics (NCHS), Division of Vital Statistics, Natality public-use data 1995-2002, on CDC WONDER On-line Database

2. United States Department of Health and Human Services (US DHHS), Centers for Disease Control and Prevention (CDC), National Center for Health Statistics (NCHS), Division of Vital Statistics, Natality public-use data 2003-2004, on CDC WONDER Online Database

3. United States Department of Health and Human Services (US DHHS), Centers for Disease Control and Prevention (CDC), National Center for Health Statistics (NCHS), Division of Vital Statistics, Natality public-use data 2003-2005, on CDC WONDER Online Database

4. Martin JA, Hamilton BE, Sutton PD, Ventura SJ, et al. Births: Final data for 2006. National vital statistics reports; vol 57 no 7. Hyattsville, MD: National Center for Health Statistics. 2009. http://www.cdc.gov/nchs/data/nvsr/nvsr57/nvsr57_07.pdf

See our Supertwins 101 FAQs: Expecting Multiples for more interesting information!

So what are the odds of spontaneous or identical multiples?

According to mathematical probabilities, the estimated odds in the United States of having spontaneous multiples (of any zygosity) are as follows: