I have what looks like a silver penny, but it's not 1943. Why is it silver, and is it valuable?

The only year that pennies did not have a copper coating was 1943. That year, they experimented with making pennies out of steel to conserve copper for the war effort (bullet casings, etc). The public didn't like the coins because they were too easily confused with dimes in change, so the mint switched back to copper the next year. (See the other FAQ on silver pennies.)

Modern pennies are a "sandwich" of a zinc alloy and a copper coating. It sounds like you have a penny that, for whatever reason, does not have its copper coating. There are a couple possible explanations:

1. It never got the copper coating at the mint. This is fairly rare, and if it's the case, the coin could have some worth as a mint error. There are collectors who specialize in error coins.
2. Some high school kids used it as a guinea pig in chemistry class. This actually happens pretty frequently. It's not difficult to strip off the copper coating if you have the right chemicals. If this is the case, the coin is a novelty, but has no collector value.

To be sure, bring the coin in to a coin shop. The dealer should be able to tell by looking at the coin under magnification whether or not the coin was dipped in chemicals.