With newer releases you will be able to configure the loopback on 3560/3750 and other Layer-3 switches.
As indicated by Amit and Adam, you are able to configure loopback interfaces on Cisco switches that are capable to run Layer3 services.
It seems your question is more inclined towards Layer2 switches such as 2960. For Layer2 switches, the answer is no.
For layer2 switches, I recommend configuring a switch virtual interface and assign an IP address to it for managing purposes.
Creating a loopback on such switch won't provide reachability to/from the loopback as the switch can't route.