I'm sure this answer won't be entirely popular with certain segments of developers, however consider if you fall into this category that perhaps your app doesn't deserve to exist on the app store. Please note that these are all implementable as code changes, no hackery or spyware like behavior required.
Basically, change the economics of your app. The User is Always Right - this is the attitude taken by one of the most successful advertising companies ever (Google). If your ads are being blocked by users, its because you suck, not because ads or ad-blockers suck.
http://books.google.com/books/about/The_User_is_Always_Right.html?id=gLjPMUjVvs0C
- Make ads less annoying and in-your-face. Users react to poor/annoying advertisement, and the seedier your app looks and becomes, the more likely they are to ditch it anyways. I don't mind apps with ads in them as long as they aren't significantly impeding the functionality, and even better I like ads which are relevant to me. (http://www.nngroup.com/articles/most-hated-advertising-techniques/)
- To detect that ads aren't being loaded, its not necessary to implement the spyware like activities mentioned by previous posters. Load an ad that has a confirmation code, and every once in awhile, insert a prompt asking for the confirmation code. The code doesn't have to be long or annoying, in fact it'd be enough to implement a captcha service with 3 or 4 letters/numbers.
(http://textcaptcha.com/api)
- In addition to detecting failure of ads to load, make better ads. Instead of using an API like mobads (Do you even realize how seedy that sounds? Mobs? Really? Are we developers, the Russian Mafia?), enter a partnership with an ad company that allows you to embed ads directly from your app. It will make your overall app larger to install, and no, you can't guard against manual modification, but the changes suggested above don't guard against that either. And this will better support any paid versions of your app, which will be much more lightweight (and faster).
- Thoroughly vet the ads you are displaying to the user, be open and transparent about your ad policies, and even allow users to inspect your ads and ad sources. The primary reason I'm ever concerned about ads is not because I hate ads, but because I worry that the poor quality developer responsible for this app is letting in viruses or other malware as well. Ask that an exception be made to the installed adblocker. Team up with ad blockers like AdBlock to get on their exceptions list. If you are a legit application, this shouldn't be a problem.
(http://www.cio.com/article/699970/6_Ways_to_Defend_Against_Drive_by_Downloads?page=1&taxonomyId=3089)
I re-iterate: all of the above changes are things you can legitimately do in code to prevent anti-ad behaviors. Ads are blocked for security reasons and visceral reactions, primarily, and sometimes bandwidth and performance, so make sure your ads don't invoke any of these problems, at the code level.
Finally I did want to touch on what Borealid said, which I re-iterated above; in the end it is a 'cat and mouse' game, because the user has ultimate authority and responsibility, both legally and morally, over their own property. A user can do whatever, including directly modify code on the fly. Of course, there are restrictions you can implement etc. but there are always ways to get around the problem. This is the ultimate problem (technically) with DRM (which is what you're trying to do). Rather than waste time and effort on this game, it is better to encourage users to keep ads around; they'll become your best, smartest anti-ad-blockers, for free.