backing image of computers over a network?

Is there a software or device to do the following:

walk into an office of say 20 computers with 3 servers. Connect a device with obviously a hard drive in it to any of the workstations. run some software which would image all the computers and save to the device. Essentially it allows me to walk off and come back in a few days if necessary.

the system should allow:

users to be able to reboot any of the servers or workstations and STILL continue the imaging
when they are switched back on

If agents are required to be installed on each pc this is ok - but agentless is better

each image should be stored in a folder with the ip address of the computer maybe some more info like the user using the workstation or the computer type and name

the images once backuped should be mountable so I can explore the files

should be able to restore to dissimlar hardware

should be able to right click and play in vmware

please assist.