I'm going to assume that the American government and American people aren't all that much different to those of other countries where the smallest currency unit was abolished long ago.
Would the government pull existing coins, say over a five year (or less) time period?
The government wouldn't really have to. Look at the huge annual mintages for 1 cent coins, just to meet current demand. If they stopped making them, the supply would dry up within a few weeks.
Would EVERYBODY (and their brother) start hoarding all pennies?
From where? If there aren't any pennies circulating, where would the hoarders get their coins from?
Would Canada follow suit and stop production of pennies also? (And vice versa, if Canada suddenly announced they were no longer going to make pennies, would the U.S. follow their lead and do likewise?)
That would depend entirely on which currency was stronger. Historic example: Australia and New Zealand. New Zealand scrapped their 1c and 2c coins in 1987. Australia did likewise in 1990. Was Australia "following their lead"? No. Australia's dollar was worth more, so our 1 cent coin retained it's buying power slightly longer. But in the end, inflation finished them both off.
Right now, the Canadian dollar is slightly stronger than the US dollar. Assuming this remains the case, and assuming all else being equal, the US cent should therefore disappear first. Countering this is the fact that "all else" isn't quite equal, since (unlike in the Australia/New Zealand example) the US and Canadian cents aren't exactly the same weight, size and composition. And either government may choose to try to stave off the inevitable for a while by making the cent out of something cheaper.
Would effect would this have on short and long term values in collecting pennies?
There are two opposing forces at work when an entire denomination ceases circulating. One one hand, if nobody sees the coins in everyday use, few people are going to suddenly be inspired to start collecting them. Very few of the half-cent, 2, 3 and 20 cent collectors began collecting them when they received one in change. So the size of the collector pool shrinks, causing reduced demand.
On the other hand, the supply shrinks too, as coins are withdrawn and destroyed, and you can no longer simply go down to the bank and get as many as you want for face value.
These two forces tend to balance out, though at any given moment one might outweigh the other, making the price go up or down. But what you almost certainly won't see is prices of bulk hoards of pennies suddenly soaring once they are withdrawn. The Australian example again: just tonight I purchased a bag of 107 Australian 2 cent coins, mixed condition, for $3 from my local coin club's auction. That's just above scrap value.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis