What is the smallest subnet one can create on AWS in the VPC?

16 IPs is the smallest range for a VPC Subnet -- /28 netmask.

For example, you could create a VPC with the CIDR range 10.0.0.0/26 which would support up to 64 IPs in the range of 10.0.0.0 - 10.0.0.63.

Then you could create 4 subnets, each with 16 available IPs using the following VPC CIDR ranges:

10.0.0.0/28   (10.0.0.0  - 10.0.0.15)
10.0.0.16/28  (10.0.0.16 - 10.0.0.31)
10.0.0.32/28  (10.0.0.32 - 10.0.0.47)
10.0.0.48/28  (10.0.0.48 - 10.0.0.63)

NOTE: See important comment below by @sqlbot. Not all 16 in range can be used for instances.