Depends.
With a meterless camera like my M3 I'll use a handheld incident meter (a sekonic twinmate) to meter when I'm faced with a new scene/ when the lighting changes. In fact, even with 35mm film cameras with meters, I use an incident meter rather than the internal meter. With medium format (and a tlr, in my case), where the shooting tends to be slower, I'm tempted to use a spot meter to ensure I have good shadow detail, but to be honest almost always end up using the same little sekonic incident meter, and in the same fashion I do with 35mm.
With digital (and AE), I always use the internal meter, doublechecking on the lcd to see if the exposure is ok. This habit has been mainly due to the tighter dynamic range latitude of dslrs when I first started shooting about 6/ 7 years ago, but to be honest now, I find the dynamic range of digital slrs much improved since then, and am tempted now to revert to incident metering, something which would not have been feasible before the last generation or two of digital cameras for me.
When I do incident meter, I find the settings rarely change, and often feel lazy for not just learning general exposure settings in outdoor situations. Indoors is a different matter, and since I shoot indoors quite a bit, I do want to pay more attention so as to be able to discern the usual range of indoor situations, which for my casual indoor shooting tends to fall in about a 3 stop range. Also, I tend to sympathise with the comment on night shooting, where you're already at the margins, handheld with a fast lens, so why meter when there is nothing you can really do (except process in diafine, which is my secret weapon for rolls shot at night).