Bytecoin [1] is intended to be exactly this. As others have mentioned, there are many imitators [2], many of which have innovations.
There are several other 'coins' other that do things very similarly to bitcoins but aren't necessarily the same. None of them, however, experience the same monetary value as bitcoins do. Here is a list of some of those other cryptocurrencies: https://bitcointalk.org/index.php?topic=134179.0
There are plenty of copy cat crypto currencies (+4 alliteration) already. But the question is, what value would a new currency provide over BTC? Mining difficulty is a feature of BTC in order to prevent all the coins from being mined before there is sufficient demand. IMO the market only needs one crypto currency and BTC is already the winner.
I'd say Ripple (https://ripple.com/) can be seen as the new Bitcoin. It's a bit different though.
Discussed extensively yesterday: https://news.ycombinator.com/item?id=6706125
There are more than a few already.
http://coinmarketcap.com/
New ones pop up every few days.
https://cryptocointalk.com/forum/40-new-cryptocoins/