This thread has gotten a bit silly. Someone else listed devices (DVR, stereo system) that are computers. Yes, that's correct. By this standard, the iPad is a computer as well.
This is the catch, however. How many people ponder whether to buy a DVR or to buy a Dell? A stereo or an iMac? Nobody would make direct comparisons like that. They may wonder where to spend their money between two different things they are interested in, but they aren't going to evaluate those items directly against a computer.
If I went around talking about "my computer" when I meant my DVR, it would baffle everyone ... even though technically, a DVR is a computer with a narrowly focused UI and input/output devices.
Calling my iPod touch a "computer" would be an affectation ... I've never heard anybody doing that, and if they did, it would be either for laughs or to prove a technical point.
The iPad is a bit further in the direction of what people think of as computers ... but still not there. This is not a put-down, it's just how it is. There are features iPads share with what people think of as computers, and features that are not shared. The form factor and UI are very different.
If you refer to your iPad as "a computer," you will end up confusing people when they see that you are actually talking about an iPad.
For those comparing power with early computers - that's a specious argument. A PCjr (which, btw, was also my first computer) is slower, has inferior graphics and has less storage than my iPod. But it was without question a computer by definitions of the time; marketed as a computer, competing with other computers for sales. It had a keyboard and monitor. It ran most DOS programs and games, with some exceptions. I did my homework on it, printed on the worst printer ever made, the IBM thermal printer.
Look, at the end of the day - is an iPad (or an iPod, or a DVR) technically a computer? Yes, of course. If you want to go around calling them computers, go ahead. Just be prepared to explain what you are talking about when you get confused looks until you drop the affectation.