If one was not worried about the amount of pins needed, which LCD setup would be the most dependable, use the least processes, be less prone to interference etc?
I'd go with SPI, I2C, Serial, if your LCD module supported it.
Some examples:
http://www.newhavendisplay.com/serial-displays-c-253.html
The only downside of the Newhaven displays CrossRoads linked is that you need to physically modify the display in order to use I2C or SPI.
See page -4 of attached spec sheet.
NEWHAVEN DISPLAY DATASHEET.pdf (1.01 MB)
I've used 16x2 parallel-interface character displays for a couple of projects in the past, but these days I usually go for 128x64 graphic LCDs with SPI interface. I've not had problems with either, but I've read a few reports on these forums of people having what appears to be noise problems when using parallel-interface character LCDs.
If it is paramount that your LCD works whatever happens, there are some options.
Be able to read the registers on the LCD, if anything seems incorrect, the code re-initialises the display.
Have a watchdog that re-initializes the display completely, rendering it to a known state. This will blank the display for a split second.
// Per.