iPhone 6, 64GB here. I started getting these a few weeks ago. It started out as one every few days, but now it's up to 5 - 6 per day. I just had my fifth one for today and it's annoying the hell out of me.
There is no immediately recognizable pattern in my usage (apps or otherwise) when I have the problem. Sometimes it's when I try to open an app, sometimes it's navigating to a web page in Safari, sometimes it's just opening an iMessage or the Mail app. I've had a few when I first unlock my phone.
I thought it was just me, then I saw a few snarky posts on Tumblr with thousands of reblogs/notes about the resprings.
The odd thing is that 8.3 has been fine since I downloaded it on release day and I haven't changed anything in months. I use the same apps I've always used, I haven't changed settings, etc. All I've done are app updates (which I do manually). When it first started I killed all my apps, did a hard reboot of the phone, and still got the resprings with only Safari running...