I bought one of the original Nexus 7 models last year and, like many others like me, found it gets slower with use. There have been ups and downs. When it installed Android Kitkat it seemed to me to be running faster, while installing the new Google Now launcher made it pretty well grind to a halt.
Recently it's been getting worse again, and last week it reached the point where I felt I had to google the problem again (on a different machine) to look for some explanation. You get a lot of suggestions doing this, some more plausible than others, and some more work than others. I don't want to have to do a factory reset, nor I am thrilled by the idea of having to root my Nexus so I can run someone's clever "speed up your device" app. (To be fair, the app may indeed be really clever, it's the rooting bit I have issues with). In truth, the most common suggestions were ones I'd already tried, or they assumed you were running out of RAM or storage space, which I definitely wasn't.
So I went into Settings and tried to spot apps that were using up suspicious amounts of CPU time. Nothing obvious, and I was out of ideas, so I resorted to uninstalling stuff I don't use much. That didn't seem to help, until I disabled (not uninstalled, just disabled) Screebl Pro. If you haven't heard of this, it's an excellent app that senses when you're holding your device and then stops it switching off the display. Now I noticed a substantial improvement, and a week later the Nexus is still running well.
I have to mention that earlier today I thought I should do the reverse experiment and re-enable Screebl Pro. This had no apparent effect on the speed, which leaves me a little confused. It may be that it was something else I tried that did the speed up, but I only noticed it after disabling Screebl. Or it may be something about leaving Screebl on for a long time that made my Nexus 7 go so slowly. Either way, I thought I'd put this out on the web. If your Nexus 7 is moving like treacle and you've got Screebl installed, it's the work of a moment to try disabling it. If it works for you, great. Otherwise I'd suggest removing some apps.