1. Me and You start a company together. We would like to split things 50/50. We setup an address such that when values are paid to it, half goes to you, half goes to me. Effectively we've created an "LLC with an Operating Agreement", but we aren't relying on political legal system / country to enforce. Enforcement is automatic and done by the network.
2. You want to setup a Trust for your kids. You create a contract that holds 10 Bitcoin / Etherum / etc. On the date Jan 1, 2035 the value of that address will be forwarded to your child's address. Again, we created a "Non-Revokable Trust" that is network enforced. No need for probate, courts, trustees, etc.