There are varying levels of gameplay depth, from the one button jump in Canabalt to the incredibly complex Yogg-Saron fight in Warcraft. A given depth of gameplay is good or bad depending on who is playing the game, how much they paid for the game and the platform the game is being played on. The PC allows for very complex/deep gameplay and I think it's obvious by now that the iPhone lends itself to 'shallow' gameplay. The iPad is somewhere in between.
It's my hope that over time we will see iPad games evolve beyond single button style gameplay. This video of multitouch gameplay in Plants vs Zombies is an indication of where games can go, it's the point where "the iPad is just a big iPod Touch" argument starts to fall apart.
Think about the size of your thumb as it compares to the iPod Touch screen. It's a huge percentage, maybe as high as 10%, but then think about the iPad. You can literally have two people using five fingers each, and still see most of the screen. Also, those 10 fingers will not max out the iPad's ability to deal with those inputs (11 seems to be the max). Those physical and technical facts make it possible to create more complex games that involve more than one person.
Now, as an aside, does "complex" = "deep"? Well, the answer is of course, "not necessarily." For me, "deep" gameplay exists when you have these three layers stacked up...
After that, anything stacked on top is flavoring and anything below is more meat. The leveling system in Call of Duty or the gear progression system in Warcraft is flavoring on top of the gameplay meat. Good design and great execution can make or break that meal of course, but (I think) you have to supply that basic framework to say the gameplay has any depth.
The iPad is uniquely positioned to allow head-to-head multiplayer on the same iPad due to its physical size and its ability to cope with a lot of incoming multitouch input. I can see an opportunity to create very social games that have much more depth than Canabalt (which is awesome, not bashing Canabalt) that you play in person. Of course, you'd have to support playing over the internet, but I think there's a great opportunity to make compelling meatspace games right now.