40/80 character LCD displays
I have an ATMEL 2051 driving a two-line 40 character LCD, programmed in assembly language.
Nokia 5510 and other PCD8544 driven displays
These small displays were common in 2G cell phones. They are 84x48 pixels, so can be used for text or graphics, like charts for data-loggers. I have one on a board from SparkFun. I plan on connecting it to my Arduino Pro Mini and/or some PICAXE. It uses a serial interface, like SPI but with an extra select between data/commands. So, I plan to use the built-in SPI functions of the Arduino, but I might also consider some libraries including one I found for PCD8544, so that I don't have to keep track of special functions for the board like initialization.
The SparkFun PCD8544 uses 3.3V, not 5V, for power and signal levels. 5V levels might damage the controller.