Happy memories
Great computer and definitely responsible for my IT-based choice of career.
Check out Chris Whytehead's museum of just about everything that Acorn ever released at http://acorn.chriswhy.co.uk/
Random stuff that was cool at the time:
AMX Mouse and AMX Super Art: The BBC micro's answer to MacPaint. Not a bad effort, very Mac-like GUI, although only four colours, small canvas and a painfully slow software pan/scroll. Some spin-offs such as the MAX mouse-based desktop which seemed to be useful for just about nothing.
Music 500 and Music 5000: Both used the same external 8-voice synth hardware (in the ubiquitous yellow/beige box) but the 5000 had ROM-based software and used loadable modules to implement a mixing desk, notation editor and program editor. All based on a FORTH-like language which was the bee's knees, allowing control of music events, definition of sound envelopes and waveforms and even system level memory poking and data structures.
Exile: For me the best game released for the BBC. Smooth multi-directional scrolling, sampled speech, physics engine. Cor!
Overheating ULA chip in the original model B. The heatsink on it seemed to only just manage the job and occasionally didn't.
Bug in the tape handling routines in the initial OS release which meant that sometimes your programs didn't save. You had to remember to load a patch before saving, or save at 300 baud rather than 1200. Forgetting to do either of those was common...
Mike Cook's hardware projects in the Micro User Magazine, e.g. foot-operated joystick made out of mercury switches, half a ballcock and a piece of board.
Granny's Garden! "That was not a good idea..." Aieeeee!