One way or another you need a server.
The way you did it before, polling a MySQL database, is a
perfectly reasonable method of doing things most of the time. The
biggest advantage is it requires no additional technology or
learning curve.
You have two primary "better" alternatives, both with cost
tradeoff:
1) Use an XMLSocket server. This is a server that you install
or create on your existing host which allows for Flash's XMLSocket
connections. XMLSocket connections will let you send XML data to
the server, and let the server push XML data at any time to all
connected Flash clients (without forcing the Flash client to
request it first, like you were doing with polling.) There are many
popular XMLSocket servers out there, and a few tutorials on how to
make your own (usually in Java):
http://www.google.com/search?hl=en&client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&hs=8El&q=Flas...
2) Use Flash Media Server. This let's you connect via Flash's
rtmp connection method. You can write server applications that push
data like an XMLSocket server, but you can also send native
ActionScript data across the connection, not just XML. You can also
send video and audio. The server application language is also
written in ActionScript, so it's very easy to learn. It's by far
the smoothest solution in my opinion, but it is not cheap.
http://www.adobe.com/products/flashmediaserver/
You can get 3rd party hosting for FMS, I use Influxis:
http://www.influxis.com/
There are also some open source Flash media server clones,
but they use different serverside language and I don't have very
positive experiences with them (but they are free):
http://osflash.org/red5