Are there any handheld vacuums (e.g. DustBuster) that come with a
power cord so that you can plug them into a wall and still use them
without having to wait for their batteries to recharge?

I'm looking for handheld vacuums that can run off of both battery
power and AC power, not just AC power.

How about this one?

http://www.brookstone.com/shop/product.asp?product_code=411884&world_code=2&category_code=63&subcategory_code=657&search_type=subcategory&cm_ven=Search&cm_cat=Froogle&cm_pla=Catalog&cm_ite=Datafeed

Hmm, I have to say that the description doesn't make it clear that the
vacuum can run while plugged into the wall.  When they say "AC
adapter," they might just mean the AC adapter that plugs into the
charging base.  It may not be able to plug into the vacuum.

This one says "Runs off of 12-18V Dewalt battery pack or 120V AC." 

http://www.wellspent.org/Product?p=423569

I'm guessing that one is actually a replacement filter for the DC500
vacuum, and they accidentally put in the description for the vacuum
instead of the filter.  I base that guess on the fact that it says
"DC5001" near the top.  DC5001 is the part number for the replacement
filter for the DC500 vacuum, as you can see from:
http://www.amazon.com/exec/obidos/tg/detail/-/B0000CCXTO/002-1534686-7287249?v=glance

Amazon's description for the DC500 vacuum (which I would not consider
to be a handheld vacuum since it weighs 10.5 pounds) is also very
similar to the description on the wellspent site, yet the price
discrepancy is huge:
http://www.amazon.com/exec/obidos/tg/detail/-/B0000CCXTN/qid=1108256533/sr=1-1/ref=sr_1_1_etk-tools/002-1534686-7287249?v=glance&s=hi&n=228013

Might I suggest http://www.dealtime.com/xPF-Euro_Pro_Euro_Pro_Shark_Intelli_Sense

The shark handheld vacuum is a corded only vacuum, running on
110/120VAC and weighs 3 lbs.

Sorry about the post. It goes against what you're requesting.
Although, if I may suggest, at the prices available, why not just get
both a corded and a cordless?