Is melting silver coins legal?

In the US, yes. Bullion dealers do it all the time, to the tune of several million ounces in 1979 and 1980 alone (during the big silver rush) http://coins.about.com/b/2008/03/12/coin-dealer-ethics-melting-coins-for-profit.htm . There's speculation the government would in fact prefer the coins go away, to increase sales of mint produced bullion coins. The bullion value of silver coins is referred to as their "melt" value--what the silver and copper will be worth once it's melted down.

It's not worth doing unless you're a recognized producer with a known hallmark, otherwise you're going to have a coin silver ingot--90% silver, 10% copper--as opposed to fine silver --.999 fine--and any bar you produce will have to have a paid appraisal before it can be sold. Also, the 1979-1980 melt alone made a lot of fairly common type coins rare. They weren't deemed special enough to worry about, and now they're much harder to find. This has impacted on collectors.

Unless you have some specific art project in mind, you're better off leaving them intact. Bullion dealers recognize them and have "bid" and "ask" rates on them. You can still buy them in "face" bags, with the face value of the coin listed (Usually $100, $250, $500 and $1000 face), but sold at current silver plus ask price.

There is a recent law that prohibits the melting of pennies and nickels for their bullion value--they currently contain more metal value than face price. You may still use them for artistic material for projects, but you may not melt them for salvage.