"Cross chaining" can occur when you use either the largest front cog with the smallest rear, or smallest front with the largest rear. The chain is stressed to cross that larger of an angle, which puts too much lateral stress on the sprockets.
You can do it for a short period with little damage, at least usually. Some bikes will begin complaining immediately.
If you do it a lot, the consequence is kinda like sharpening your sprockets. The chain begins to wear them down, leaving them thinner and more pointed. It damages the chain too.
For the most part you don't need to do it. There will be gears off of the middle crank, or the smaller crank on a double, that will be near duplicates of the large front to large rear.
As to question about the lack of a granny gear, that's more a question of your own riding condition. A lot of cyclists do fine with compact doubles, where the lowest gearing is around 39:26 (assuming a 12-26 rear cassette). That's a reasonably low climbing gear for many. For others of us it isn't nearly enough. My hybrid's lowest gear is 26 in the front and 34 in the rear - a great grandmother gear.
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Last edited by Tom Bombadil; 04-19-07 at 07:46 PM.