Here's some features I'm planning on:

• Auto-ranging
• True RMS
• Very fast response times
• 16-bit resolution (30,000 count) at 50 k samples / second (16.7 k / second if multiple channels are being measured), and 12-bit resolution (2000 count) at 1 M samples / second (using the ADCs in a STM3F373)
• Data logging (probably via USB)
• Signal generator (may be USB-only, or whatever other means logging uses)
• Power measurement (measuring both current and voltage at once)
• LCR meter
• Li-Poly battery
• Any extra GPIO lines on the micro will be broken out – probably enough for a very basic logic analyser

I'm also aiming for better than 0.1% accuracy (more details about how I expect to achieve this another day...), but if I can only get 1% that'll be OK. This (0.1%) is 30 times less than the resolution (0.003%), but the extra resolution is still useful (and reduces any errors from the analog-to-digital conversion). By way of comparison, cheap multimeters (I have three particular models in mind) may have an accuracy of 0.5% to 1.5%, while having a resolution of 4,000 or 0.025%, to give a resolution 20 (for 0.5% accuracy) or 60 (for 1.5% accuracy) times higher than the accuracy.

Of course, all the normal features will be present as well (current, resistance, continuity, diode test, frequency, duty cycle...).