Instagram’s Hyperlapse works well in good light to stabilize handheld video. It was developed for time-lapse shots, but at 1X it does the same thing for normal speed.
Now there’s a Kickstarter to add the technology to any GoPro or DSLR. Very handy. Only downside on the iPhone is Hyperlapse reduces 1080 filming to 720 — which is a version of what post-production image stabilization does, anyway, but not usually with such a large jump down in resolution. An earlier araratfilm.org post has some tips, including how to force 1080.