As long as you use a digital meter (not analog), you can measure most loads with reasonable accuracy.
Just because a meter is digital doesn't mean it's true-rms.
There are two principle load types: linear and non-linear. Linear means that the load draws current over the complete cycle of a sinusoidal waveform. Non-linear loads draw current only in short pulses over the cycle, and because of this, distorts the waveform by adding harmonics.
Linear load examples include a heater, an incandescent lamp, or an induction motor running directly off an ac line. Non-linear loads include most electronics (Variable frequency drives, UPSs, computers, etc.) as well as fluorescent and HID (high intensity discharge) lamps.
A regular digital meter can measure linear loads with reasonable accuracy, but it can't accurately measure non-linear loads. For that, you need a True RMS meter.
For more information, Fluke has an application note on True RMS (.pdf) »