One of the best gifts we got when Willow was first born was the Papasan Swing. It was a gift from her lovely aunt and she loved it.
The really great thing about this swing is that it can swing either side-to-side or back-to-front. And the mobile is cute because it moves and twirls (if you want it to) and you can choose whether or not to play music. Willow loved sleeping in this swing.
The ONLY drawback for this swing is that it takes batteries. Yes, it is mobile but I would have preferred something that plugged in. But that's just us and I don't have any idea if there is an infant swing in existence that plugs in.
