Basically you could find commercial products, sharewares and freewares. The commercial ones were often referred as the "Full Version" and could be pricy. Sharewares were good enough to enjoy for a while, especially games, and could give you a good idea of the product before buying it. Freewares were often copies of already known softwares but offered a great alternative to the real stuff.
With the arrival of the Apple Store and Google Play, everything changed. An app is now labeled as "Free", meaning it is limited and contains ads. A regular paid app can be limited in some way and includes some in-app purchases to extend the features. A "Pro" app is normally the complete solution but can still have some optional features that you can buy. Basically, a lot of apps are sharewares disguised a "Full Version".
Games do implements the new "Shareware Model" more than anything else. It's getting harder to buy a complete game that does not need some kind of currency to get to the next level.
Real money has been converted into virtual currencies to hide the simple fact that it costs more dough to play. Gems, gold coins, rubies, diamonds and other elegant and shiny tokens are required to get to the next level, acquire more advanced items or to unlock some cheats.
If you want to be #1 at any game, just buy some diamonds and you'll be the most famous guy on the planet, for a few minutes... No need to practice, no need to start over. Just buy some power-ups.
Is it annoying me? Not that much. But I do get annoyed when I discover that I need to buy coins just to complete a level in today. Waiting 24 hours to grow a more productive crop or to build a new bridge just drives me nut. I want to play now because I have the time NOW!
Ads can be annoying and distracting. Limited features are understandable as the devs do need to eat too. The "Waiting-Game-Or-Spend-To-Play-Now" feature is more than annoying and will result into uninstalling the game, or the app.
Sharewares are definitively not dead...