I've been asking around for a few months about having "@replys" pushed to my iPhone from Twitter and the only thing I could find for free was Echofon (but that was only when the other person also used it). I wasn't all that impressed with Echofon and now exclusively use Twitteriffic.
However a few days ago, I read an article on TechCrunch that talked about Boxcar push notifications and BAM, it's free and it works perfectly.
Download Boxcar from the app store and make sure to set up Twitter as the only service. See, the first service is free - the rest (Gmail, Facebook) range from $0.99 to $1.99. Once you set up twitter, you will start to get the same push notifications you see above.
As you can see here, you can also select your Twitter Timeline, Mentions, DM's, and RT's to be pushed to you. All for free. Other settings include sounds, badges, and Private Alerts. Private Alerts just let you know you have a notification without the detail.
Let me know if you were able to get this set up and what you think about it.