That depends on what you are measuring. When I am measuring the temperature of the air in a house or outside, I also measure the relative humidity (RH), which will take several minutes to stabilize with a digital Temp/RH meter. If I am measuring the temperature rise across the heat exchanger of a furnace, I use a digital Accurite food thermometer. In a moving air stream they react fairly quickly. I use the same thermometer for measuring the temperature of the hot water at the tap, and it reacts quite quickly with liquids.
That's good to know. I am usually looking for a quick read on ambient air temperature. I eventually purchased a Testo 605-H2 Humidity Stick, which works fairly well but still takes a few minutes to stabilize. It does well in a moving air stream and has a nice feature of a built-in shield in case I can't get a hole around a bend from the heat exchanger. I haven't tried it on a liquid, and I'm actually not sure it's built for that. I'll have to check the manual.
Most of the temp/RH meters come to a reading more quickly if you wave them around in the air a bit.
I don't think the Testo is intended for liquids, but I could be wrong...