There have been many tweets floating about requesting Twitter applications for iPhone OS 3.0 that sport push notifications. I am writing this post to let you know that it's not as easy as that.
Firstly, the reason is because this requires the direct cooperation of Twitter. With the thousands of tweets being posted every second, it is important that Twitter have some mechanism for notifying people when tweets are posted that are relevant to them. Currently this does not exist; getting data from Twitter is an entirely pull-style technology. You need to poll for new information.
Secondly, Twitter are unlikely to implement push notifications directly in their own service because it's just not profitable for them to do so. In fact, it is very likely that developers are going to have to pay for push notifications in the future (although it is more likely that the cost will be levied onto the users). The only other option is for each client author to maintain their own server to watch the tweets and send push notifications like that, but this is very impractical: typical application authors do not have the huge amount of server resources available for this kind of work. We're still talking thousands of tweets per second. That would require ultimately huge bandwidth and processing time. It is a hideously inefficient way of doing it.
So, the moral of the story is, don't get your hopes up, kids. Twitter is most likely still a very long way from push notifications on the iPhone.