After patiently waiting for Google to re-supply the Nexus 4 I finally got my own one February 4th. It is the best phone I’ve ever owned. The bumper wasn’t in stock, but I so liked the look of the phone I chose not to have any kind of protective case.
Three months later one warm Spring evening, I was chatting outside a pub. As I pulled the phone from my jeans pocket it slipped and hit the pavement face down. As the pictures show it must have hit at an angle, but the impact was sufficient to crack the screen badly1. 
Interestingly there were no scratches, just the glass itself was cracked. The phone turned on, and even the screen itself was working. However, the digitiser was not - a big problem as I could no longer interact with the phone. I’d never broken a phone before so this was a first2.
One bonus was that I was using facial recognition to unlock the phone, so I could get that far. A second bonus is that I had debugging enabled on the phone due to my Android development work.
I could connect to the phone with adb shell, sending keystrokes like:adb shell input keyevent 66
which would send an “enter” keypress to the device3.
By using the arrow keys (19-22) I was able to verify that all the other functions on the device worked fine, from the camera to phone calls.
Reassured, I did a search and found a website called “Spares LG”4 that sold a replacement digitiser. (It comes as one unit with the LCD.) The cost was around £70 which seemed to be the most cost-effective option available.
When the replacement part was delivered I set about doing the repair. The primary source was a YouTube video called “Nexus 4 LG E960 screen replacement”5. I watched the video first as what I wanted most to avoid was damaging the device in the act of dismantling it for repair.
The entire process went without any hitch, taking about 40 minutes. The worst bit was prying the battery out as it had been glued in. (I hate prying anything.) After re-assembling the phone everything worked - except the proximity sensor which reported the phone as being in permanent darkness. This meant that once I’d made a call with the phone next to my ear, the phone screen would stay off even after I was finished with the call. I had to re-open the case and reposition the little rubber “cup” alongside the headphone jack that the proximity sensor nestles into. (The sensor needs an unobstructed view out of the case.)
End result: I’m very pleased with the repair. It looks as good as when it first arrived.
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P.S. I’m now trying a “gel case” to protect it from any future drops. More than anything it should be less slippery to the touch now.
P.P.S. Still love it.
P.P.P.S. A special mention for my Nexus S. Still going strong while the Nexus 4 was out of commission. You can see it in a reflection in the image of the undamaged back of the phone.
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[1] Photos of the damaged Nexus 4: before and after the repair
[2] Curiously I took it in my stride. I suspect a younger me might have been quite upset.
[3] http://stackoverflow.com/questions/7789826/adb-shell-input-events
[4] http://www.spareslg.com/lcd-e-touch-lg-nexus-4-lg-e960-acq86270901.html
[5] http://www.youtube.com/watch?v=MFzbfeY_xTQ “Nexus 4 LG E960 screen replacement”