It all depends on how you want to animate! Flash and Toonboom are both great for hand-drawn animation, but unfortunately they're a bit pricey. Don't be too intimidated by Flash -- once you get used to the timeline and the drawing tools, on a basic level it's really no more difficult than drawing something and moving on to the next frame. The animation workflow is simple and straightforward; the reason the program looks complicated is because there's a lot you can do with it besides animation. Although I've never tried out Toonboom, as far as I can tell it's a lot like Flash but designed specifically for animation, so it's likely a bit easier to use for that purpose.
I've searched pretty hard for good free animation software in the past, and Pencil is probably going to be your best bet for hand-drawn animation if you don't want to buy anything. There are lots of others and I'm sure more are being created as I write this, but the other ones that I've tried all seem to have drawbacks of some sort or another. EZtoon is wonderfully simple and Plastic Animation Paper is great for more traditional animation, but you can't really use color in either of them. Synfig looks awesome, but I don't think I'd have the patience to learn how to use it either =P
To answer your other question, it would probably be a bit more cumbersome, but you certainly could make Pivot-like animations with Pencil by using the line tool. To my knowledge, Pencil doesn't have any way to make a figure with 'bones' that you can use to reposition them like you can in Pivot, but if you just drew things with straight lines, you'd end up with something that resembles the segments that Pivot uses.
Also, a bit of advice: don't let yourself feel disappointed if your first animations in a new program don't turn out as good as you'd hoped! A lot of animation programs (Pivot and Stykz, for example) are very similar, but the differences between them can be surprisingly disorienting.