What do Litecoins offer over Bitcoin?
First of all, Litecoin uses the Scrypt hashing algorithm instead of the SHA256 hashing algorithm. Scrypt is much more CPU-friendly, which means that you can mine it easily at home without any custom hardware.
Another notable difference between Litecoin and Bitcoin is that the Litecoin network has the capacity to produce four times as many Litcoin units compared to Bitcoin (84 million).
And last but not least, Litecoin is scheduled to produce blocks four times as fast as for Bitcoin (on average every 2.5 minutes), thus allowing potentially for faster confirmation for merchants. However, I'm not quite sure whether those differences are really enough to set LTC sufficiently "apart" from BTC in order to be successful long-term. Nevertheless I just started experimenting with LTC for fun.