Got the same message:
Sept 19, 2011 @ 12:01 MDT - You've won 200,000 Air Miles, Select 1 to accept.
This is a known vacation marketing company that is doing this.  Here's the info I was able to get after stringing them along (for the SECOND TIME in as many months):
Sunset World - Parent company representing 4 or 5 different RCI vacation resorts.  
Vacation packages are sold under the company names: Tropical Travel or Paradise Destination.
One of the managers: Robert Hanson
The 'deal' : They legitamitely appear to sell vacation packages. You do NOT receive ANY reward miles - you get a "discount" off the package price (but only if you buy during that call). So while this truly may not qualify as a scam, it is misleading & damned annoying.

VALID Phone Numbers for the company:
1-+1 866-760-1843  (reservation Dept)
1-+1 800-961-8354  (Customer service)
1-+1 800-490-7452  (Main # with links to all depts)

On a completely separate topic - did you know that each call to a toll free number costs you nothing, but costs the company at the other end $$/call.

Got the same message:Sept 19, 2011 @ 12:01 MDT - You've won 200,000 Air Miles, Select 1 to accept.This is a known vacation marketing company that is doing this.  Here's the info I was able to get after stringing them along (for the SECOND TIME in as many months):Sunset World - Parent company representing 4 or 5 different RCI vacation resorts.  Vacation packages are sold under the company names: Tropical Travel or Paradise Destination. One of the managers: Robert HansonThe 'deal' : They legitamitely appear to sell vacation packages. You do NOT receive ANY reward miles - you get a "discount" off the package price (but only if you buy during that call). So while this truly may not qualify as a scam, it is misleading & damned annoying.VALID Phone Numbers for the company:1-+1 866-760-1843  (reservation Dept)1-+1 800-961-8354  (Customer service)1-+1 800-490-7452  (Main # with links to all depts)On a completely separate topic - did you know that each call to a toll free number costs you nothing, but costs the company at the other end $$/call.

(780) 739-8787 Got a call from this number the message saying its from Air Canada and I a winner of 200000 Aeoplan miles and press 1 to clain. When I call back I got engange tone

Got mine in Spanish, translated to: "Since your a valuble AT&T customer we are happy to".......I hung up. Don't like recorded sales messages especially during dinner. 17:34 CDT

Not sure if I just made matters worse or not, I phoned the customer service number in ScubaNut's comment and asked the fellow to add me to the do not call list.  He was nice enough, said he would.  Huh.  Probably not that easy eh?

called @ work in BCautomated message says you're the winner of some AirMiles....i hung up