I use Pomodoros with some success, but I would really like to be able to easily track how many and when I do them. Is there an app that keeps a log of start time and stop time (if it was stopped prematurely)? Preferably with an easy way to export?
AFAIK there are no Android Pomodoro apps that keep detailed statistics. Most Pomodoro apps I found on Google Play are just basic timers.
I think the app that comes closest to your needs is Pomodoro Master. It keeps track of the total amount of pomodoro's today, this week and this month. There is also a paid version but I'm not sure what the extra's are.
A similar app is Pomodroido, which offers more or less the same as Pomodoro Master but without the month statistic. However, on Google Play it says that they are working on analytics and something called "Pomodoro exportable" (not sure what they mean by it, but maybe export function?).
I haven't tried any Pomodoro software on my computer. From what I've read on this Productivity question it seems like Pomodairo might do the trick? If you're on a Mac, you might also want to look at My Little Pomodoro (paid software)
I use http://www.pomodorowebapp.com/ for what you describe... keeping track of how may pomodoros I do on different tasks; it shows progress graphs too :) Unfortunately doesn't work on my android phone when the screen is off, but works in any standard browser.