SQL Cluster without a shared disk. Possible? Is it possible to create a two node cluster using two basic network servers that only have local disks? 

One will act as an idle standby server.  Without knowing too much about clustering I'm not sure if a separate shared disk array is required.

If so, is it possible to use a DAS setup, or does it have to be a SAN that supports clustering?
I am afraid that this is not possible. Clustering works on the basis of resource ownership and acquisition; so anything that is not accessible to all nodes in the cluster cannot be used.

If shared storage is not an option for you then have a look at using mirroring which does not require storage to be shared across multiple servers. You could even use a witness server to automatically fail over should the primary become unreachable for any reason:

DATABASE MIRRORING

http://msdn.microsoft.com/en-us/library/ms189852.aspx

SQL CLUSTERING CONSIDERATIONS

http://msdn.microsoft.com/en-us/library/ms189910.aspx

I hope this helps you.