I would like to buy some premium imported Japanese sake. What are some
good online sites that will allow me to place an order for various
brands of sake, assuming that it'd be shipped to me in the United
States?

Dear Q3augustus, 

In addition to the suggestions of my esteemed colleagues, let me
suggest some of online Sake importers/sellers. Please note their
location, because of the limitation on the shipment of alcoholic
beverages:

Beekman Liquors <http://www.beekmanliquors.com/sake.htm> from New York
has several types of premium Sake, including the famed Kamoizumi.

Internet Wines & Spirits <http://www.internetwines.com/> - has dozens
of types of Sake, not all of them imported from Japan, though (neither
all of them what I shall call "premium", but they also have several
good types)

Beverages and More <http://www.bevmo.com/productlist.asp?area=wine&category=20170000&catname=Sake&leftmenu=Sake>
have several types of Sake and offers special prices to members. Ships
only in the Western states.

Mad Wine <http://store.yahoo.com/madwine/sake.html> ships to
California, Colorado, Idaho, Illinois, Iowa, Missouri, New Mexico,
Oregon, Washington and Wisconsin.

I hope this answered your question. The search for the sake shops
included:
- Searching for names of renowned sake brands, in Google (with the
addition site:com for .com sites, and the screening to English
speaking sites only, to avoid Japanese sites)
- searching for the term "Sake" in Froogle (it yielded much more
results than mentioned here - see
http://froogle.google.com/froogle?q=sake).
- Searching for terms such as "imported sake" in Google.com 

If you need any further clarifications on this answer, please let me
know. I'd be pleased to clarify my answer before you rate it.

http://www.esake.com/

"This site is devoted to premium Japanese sake (nihonshu). We offer a
large and growing collection of online resources, including reviews of
small family-run Japanese brewers, over 100 articles by sake expert
John Gauntner, and tips on where to buy premium sake in the USA and
elsewhere."

"eSake does not sell sake, but the brewers introduced here do. Their
sake can be purchased online in the USA, and at select restaurants and
retail outlets in 32 states. Please visit the Sake Store for more. "

The Sake Store has a list of places that sell online to the USA
http://www.esake.com/Store/store.html

You'll find a nice selection of sake at Bevmo.com:

http://www.bevmo.com/productlist.asp?area=wine&category=20170000&catname=Sake