Why is the $ on the left, and the ¢ on the right?

Because that’s the way God made it.

[disclaimer: the following is pure speculation]
Could it be so as to avoid confusion with dollar value? For example, if you wrote ¢0.01 is that 1 cent or 1/100 of a cent because the figure before the . is the value referred to on the left?

I tried wiki’ing, but didn’t find anything to suggest why it’s this way, but did find that there is no set standard for the Euro , although I’m fairly certain all Euro-zone countries apply the same practice of symbol placement – and come to think of it, the same goes for Danish krona (Kr./DKK 0,01 vs. 1øre)

Maybe because dollars are on the left of the decimal point and cents are to the right?

more personal speculation:
I can think of no more “reason” for US currency symbols than usual and customary practice.
wildflower’s response made me wonder about the history of the ”$” and cent-symbols (sorry, I can’t remember the right keyboard shortcut for the cent-symbol…). I am curious if there is any relationship between cent-symbol and ”%”. I think ”%” may have started out as a shorthand for “divided by one-hundred”.
Could cent-symbol have started out as a shorthand? I seem to remember that the “C” in the cent-symbol comes from the Roman numeral “C” which is one hundred.

The $ comes from peso, if I remember right. I’m sure that I could wiki or google it but I’m too lazy this morning. No idea where cents symbol came from though.
As for why $ is in front and cents is after probably came from England – £5 – 5p.
Why they started doing it, I have no idea.

“When writing currency amounts the location of the sign varies by currency. Many currencies, especially in Latin America and the English-speaking world, place it before the amount (e.g., £50.00); many others place it after the amount (e.g., 50.00 S₣); and, before they were abolished, the sign for the Portuguese Escudo and the French Franc were placed in the decimal position (i.e., 50$00 or 12₣34). The standardized European default placement, used in absence of a national standard, is that (€) is placed before the amount. However, many Eurozone countries have sustained or generated alternative conventions.

The decimal separator can also take local countries’ standards. For instance, the United Kingdom often uses a middle dot as the decimal point on price stickers (eg., ’£5·52’), although not in print. A comma (eg. ‘5,00 €’) is a common separator used in other countries.” (Wikipedia)