Oh man, you've just opened the floodgates. I just love to geek out on this topic. :)
I've been in the adult industry for almost a decade- both in "hardware" (sex toys) and software (mobile app store, video streaming). What sort of innovations are you looking for? Content, social, tech?
A sex toy company I find innovative is Revel Body. Most vibrators use a rotary motor that spins an off-kilter weight to create the vibration. Revel Body developed their own patented linear motor that uses magnetic fields of alternating polarity to slide a weight back and forth in a linear motion. It's super quiet, more powerful and last longer than the older motors. They also designed their own chip to give the user precise control of the frequency and speed. I would have loved to have used RB's motor in the toys I designed.
Lovepalz has the Zeus and Hera toys that couple hardware with software for long distance partners. Minna toys have pressure sensitive control panels.
The folks at Utherverse created an immersive adults-only virtual world. I believe they launched a major overhaul to their platform last month. They've also built a VR compatible platform specifically for the Oculus Rift universe. In terms of VR porn, Utherverse is at the forefront.
For software, I think we tend to look at consumer-facing sites and products, but there's a wealth of tech innovation happening behind the scenes. SendFaster, while not an adult company (but a tech co that powers a number of adult sites, mine included) has amazing TCP acceleration and image compression software.
While not a startup, Streamates developed their own live streaming technology that's used by millions of visitors daily.
Speaking of my company, I co-founded the MiKandi Adult App Store. We launched almost 5 years ago as the first adults only app store, before Android really hit it big. Being early adopters of Android and one of the few third party Android app stores at the time, we really dove head first into it. Under our belt today, we've got app distribution, mobile video streaming, in-app billing, notifications, DRM and content management, and soon-to-launch an ebook reader, mobile game creator, and comic reader and creator. We've tried to push other tech forward but are usually shot down soon after launching them- our Google Glass adult app, Tits & Glass, and our third party Chrome app store, MiKandi Mint.
As far as the problem we're trying to solve, it's less about a problem in the adult industry as much as it's a problem in the mainstream tech and banking industries, which is being discussed a lot here. I wrote about the hostile business world here: http://modelviewculture.com/pieces/sextech-startups-in-a-hos...