I've been spending a lot of time thinking about this subject. It's the same thing the industry has been talking about for the last several years, only with different terms. The popular adjectives are "casual" and "core", which describe both games and gamers alike, but in very broad, unspecific terms. Casual is usually synonymous with Farmville, Bejeweled, and other mindless time-killers that require little skill or commitment from the player. Meanwhile, the other end of the spectrum demands twitch reflexes, and a high tolerance for violence, as most "core" games are male power fantasies that usually involve guns, cars, and you being a hero. In either case, most publishers and developers are thinking in terms of demographics: which subset of the gaming population are we trying to appeal to, what's the revenue potential of "A+B+C", etc.
If you ask me, too much energy is spent thinking about games and gamers in these broad terms, rather than getting to the heart of why people have these different tastes. It really comes down to accessibility. There are a lot of ingredients that collide to determine how accessible your game is. Is it stylistically grotesque, or cute? Is it incredibly complicated, or mindlessly easy? How long is a typical play session? It's no secret that most of the big hits on the App Store tend to be very simple - they take about 5 seconds to learn how to play, and very slowly ramp up their difficulty and mechanical complexity, they're usually pretty cute, and you can play them for as little or as much time as you like.
But its not necessary that every game has to be incredibly simple in order to lure people in successfully - depth and accessibility aren't mutually exclusive, because not everyone's taste falls perfectly into one category or another. I've seen my own tastes shift as I've gotten older - I used to forgive a lot of tedious bullshit that games would present me with, but I'd muscle through it. These days, I'm a lot less forgiving. The goal is to simply avoid putting unnecessary obstacles in the way of people's fun. Don't bombard them with information too fast, don't subject them to badly written soap opera cut-scenes or huge amounts of travel time, keep the visuals appealing, don't have ridiculous loading times, and keep your input super responsive. It seems obvious, but you still see these mistakes being made today by huge, multi-million dollar budget games.
There does come a point, however, when some players will get turned away by too little complexity. For lots of us, a game has to offer some resistance, or we don't feel like we're accomplishing anything. Some of my favorite games present challenges so overwhelming that they repel most people, but that in turn adds to the payoff if/when you surmount those challenges. There's also a certain joy to be had in simply exploring and learning about a game's rules from experience, rather than being handed all the information you need to succeed, but that's asking a greater level of mental commitment from the player.
So this is the real question for a developer - where does your game live on this spectrum? How much will your game suffer in terms of fun and depth if you choose to make it too accessible? When you omit something, are you compromising the product, or just trimming the fat?
I think I've walked this line with mixed success over the years, with Battleheart being the one I'm most proud of. I feel like it has a pretty good amount of tactical depth, without being overwhelming when you first start. It requires some decent reflexes, but it's no "Ninja Gaiden". You get to kill things and kick ass, but its still cute and kid-friendly. For my next game, I'm aiming to push things a little further towards the "depth" side of the spectrum and see how things go. Mobile app consumers represent a huge and diverse group of people, so there's no question that there's an appetite for something a little more involved and complex.
