How can I wipe data with no display ( e.g. magnet )? I dropped my phone and broke the LCD. Now I can turn the phone on ( I feel the little quick vibrate that happens when you power the phone on ) but I have no display at all.

I got a replacement with the insurance plan, but I need to send the broken phone back. How can I wipe my data? Can I just rub a magnet all over it? How big a magnet?

Any other options? I thought about trying to navigate to the bootloader's reset function without being able to actually see what I'm doing, but I won't know if I succeed or not, and there are a few menus to navigate.

I also was going to ssh to the phone, but apparently I never made it so sshd starts automatically ( doh! ).

Any ideas?
Go to recovery mode of device and wipe data from there. In recovery mode, you need to work with physical keys (touchscreen doesn't work in this mode even in normal situation). Generally, volume keys are used for navigation and home key for Enter/OK.

How to click wipe data option when I can't see it.
See YouTube video of your recovery mode or check it in your friends' device. You can really do it after learning series of keys which needs to be pressed. E.g. down key 5 times, then home key, then down key 3 times and again home key.

How to ensure I am in Recovery Mode when I miss it many times even after proper key combination?
After you think you should be in recovery, leave device idle. If you hear boot music, remove battery, re-insert it and try again.

How about SSH/FTP?
Its very difficult without working touchscreen because it needs particular app/service running on device.

What about other physics based methods like magnetic wiping?
What you see in hacking movies can't be applied in real world. Particularly, powerful magnets can affect data on hard disks. Device storage doesn't store data using magnetic attributes.
Even if you find something which could wipe data such way, I'd strongly not recommend it because there's no reason why it can't damage hardware capabilities if it can wipe data from flash storage. In the last, this part is off-topic on this site.