In the olden days with our racks of Dell servers we used to have the luxury of the iDRAC card - Integrated Dell Remote Access Controller (I often wondered what the acronym meant!) - other manufacturers like HP, IBM, etc would all have something similar. Essentially, it lived on a different network connection, and gave you remote access to the machine - even when things had gone badly wrong. You could even mount ISO files over the network - meaning you could install Operating Systems over it - great for when things had all gone a bit wrong, or even for upgrading with some peace of mind that you could access the machine regardless of what happened. When working with XenServer it was a pretty useful way of upgrading between major releases (for some reason it didn't allow remote upgrades).
In the virtual server space, one of the great things about Linode was LISH - an out of band access tool to your virtual server instance. Again, this provided console access - great for resolving boot time issues, allowing you to drop into single user mode.
But, with EC2 there isn't yet an equivalent - if you've used an EBS backed instance then you can stop your instance, mount the volume elsewhere and attempt to diagnose and fix any issues - there is a guide over here. This doesn't allow you to drop into single user mode, and is a bit more effort - it would be great if Amazon could provide something more like LISH...
Why would it be useful? Sometimes you can be a dork and make changes to the system that don't become a problem until you restart - changes to fstab are a classic example - you can see the log telling you to press a button, but you can't get to it. As above - there are workarounds, but it would be great if you could jump straight in and connect to the console. Likewise when creating new AMIs - it would aid debugging of issues to have console access and single user mode without having to start over or mount/unmount volumes from other instances.
So, Dear Amazon Web Services.. please give me a console!