Can Android apps spam you? Yes, they can.
It's no strange concept that free Android apps generally make their money by displaying ads. I doubt most people would be bothered by the idea. Game play is interrupted for a few moments of Angry Birds to view an ad - or an ad blocks a corner of the screen, and then we're back to regular game play as usual. Maybe there's a link to a website or a video, and if you accidentally click on it, your browser opens to some advertiser's site. (Assuming the click was accidental.)
A more annoying form of ad has links to download a paid or free app - You like talking lump of coal? Why not download talking toilet paper? Usually the danger there is that if you accidentally click on the wrong thing, you end up downloading something you didn't want. It's super annoying if you have kids, because they'll always click on those dang things. In the end, both of these ads are more inconvenience than anything else, and most of us are willing to live with them as a price to getting free apps. Buy the paid version if you don't want your play to be interrupted with an ad.
Ad network developers, however, have developed ever cleverer schemes for making people click on ads. Not content with interrupting game play, they've come up with ways to make you see ads when you're not even playing the game that came bundled with the ad network. There are ads that give you notifications and alerts when you're not playing the game or ads that appear to download extra apps onto your desktop. We'll discuss these annoying spam ads and what you can do to stop them.
Push Notification Ads
Push alerts, push notifications, and notification spam are ads that take advantage of useful functionality in Android to do some very annoying things. Push notifications or push alerts are notifications that appear when you aren't actively using the app. The app is generally on in the background and checks for updates. You want some of your apps to do this - otherwise you'd never know you had new email messages. Push alerts can be legitimately used to let you know that there's an update to a product, that you've got new email, or that there's a special on the type of e-book you like to read (although this last bit borders on spam already.)
Push notifications can also be maliciously used to try and sell you products you don't want or to actually fool you into thinking you're clicking on a legitimate product update alert when actually you're launching a process to sign up for a service that will cost you money. There's a lawsuit right now against AirPush and GoLive Mobile alleging that they're doing just that.
Icon Spam Ads
Another type of ad - one of my least favorite - is the icon spam ad. This is an ad that shows up on your home screen as if you'd downloaded a new app. You didn't. They're showing up because an app you've legitimately downloaded is tied to an ad network that makes spammy icons appear on your desktop. Some of these ads may show things like "market" that don't actually go to the Google Play market or other deceptive and shady icons. You can either manually delete them (and they'll keep coming back) or delete the app that is producing the ads. My vote is to delete the offending app.
Getting Rid of Spamming Apps
My current recommendations for ad blocking software are AirPush Detector or Lookout Ad Network Detector. These won't delete apps for you. Both ad detecting apps will just tell you which apps you have that are attached to known spamming ad networks and let you decide where to go from there (my vote is the trash can with the offending apps.) There are countless other ad blockers as well, although pay close attention to the ratings and review comments to make sure you're not accidentally downloading a wolf in sheep's clothing. Some ad blockers also require that you root your phone in order to use them, and that may be more you want to do.
I suspect that these recent developments in annoying spam ad technology will prompt some changes in Android and the Google Play market. Eventually we may see spammy apps required to disclose exactly how they plan to advertise before you download the app or an outright ban on the more annoying forms of ads like icon spam.