The best available by far and I've tried many.
Let me start by saying I didn't think anything would ever be able to top the Zagg Invisible Shield HD. This does, far and away. If you're one of those people who hates screen protectors, this looks and feels like there is absolutely nothing on your phone screen at all. Fingerprints wipe away very easily and I have never had a problem with bubbles or with it lifting up. I had it on my S4 for 5 months. It worked perfectly and still looked like new, so I knew when I got the Note 3 I had to have it.
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It is pricey, but when you're buying a high end smartphone, so more than worth it. It works with every case I've tried, Otterbox commuter and defender, Mophie, Speck, Lifeproof (has to be the NUUD with the open screen though). I do recommend having it installed at the store if possible and they do it for free.