FWIW - I would be annoyed with anything more than a weekly update in most cases. However, in some cases, I would be very happy with a daily update. Without knowledge of your app/use case, it's hard to give a more solid opinion.
In terms of giving them a choice, yes, that's definitely something we've got on the roadmap, but I'm wondering if there are best practices/frequency to abide by in the mean time.
Examples: 1. Facebook/LinkedIn: Send me an update every day if you want. We can even restrict those updates to "new features" -- e.g. Today, LinkedIn released updated mobile apps -- I read about them on TechCrunch. I would have been happy to get that as an email.
2. TaskRabbit/Box - you can stop sending me emails, or send them once a quarter or get them to me some other way (like when I visit your site or launch your app). I don't rely on the service enough, or use it enough, to need regular updates.
3. Banking - You got some new features for me - let me know weekly or monthly. Same goes for Rewards/Miles/CreditCard, etc...
4. ANY account/service in which I'm active and you have a feature that you somehow KNOW I'm going to want/need - Notify me immediately. I don't know how this could be found offensive if it's something that is very relevant.
ALL of the above are MY preferences. For any given example, I'm certain that different types of users will have different preferences. That's why I suggested giving the customer the option, with sensible defaults.