Bitcoin uses proof of work to secure the network, Ripple uses a global consensus system and PPCoin uses proof of stake.
Are there any known alternatives to the above methods?
Another alternative is proof of burn.
A really quick answer is this: The proof of work system is a solution to the distributed synchronization issue; in another guise it is called the Byzantine Generals' Problem. Thus, any solution to this problem is an acceptable alternative, however the proof-of-work solution is particularly suited to distributed systems.
You can read Satoshi Nakamoto's discussion of this here.
I have been researching on blockchain for sometime now and some of them I found are a mix of some existing and some proposed.