Here’s a simple example of calling the vSphere REST API using curl. These commands first authenticate to the API which creates a vmware-api-session-id cookie which is stored to cookie-jar.txt then makes a request to get a list of VMs:
curl -k -i -u firstname.lastname@example.org:password -X POST -c cookie-jar.txt https://vcenter/rest/com/vmware/cis/session curl -k -i -b cookie-jar.txt https://vcenter/rest/vcenter/vm
NOTE: Use with caution as your credentials will likely be caught in your command line history!
Here’s a related post on vSphere SDKs.