DC motors don't work well at low RPMs. They stall and have horrible torque. (i.e. they can't turn very hard) So people have created gear motors: motors with integrated gearing. The result looks like a slightly bulkier motor, but one that has low RPMs and high torque. If you were to take apart a running a gear motor, you'd see the motor part actually runs at several thousand RPMs, but it's geared down to something like 60 RPM max.
A common specialized one is the standard hobby servo, which has some additional electronic bits but is fundamentally a gear motor. Check out any place that sells motors for robotics or surplus electronics and you'll see several different gear motors to choose from.
DC gear motors are controlled just like normal DC motors, so an Arduino motor shield works just fine with them.
For industrial grade applications, a more typical arrangement than the conventional servomotor, is a suitably geared down 3 phase motor, with either end-stop detection, or some form of position encoding, controlled by a HVAC (or main line voltage) control circuit, either switched or PID based.
For instance, in railway locomotives, while the pantograph seems an ideal candidate for a big servomotor, that is rarely if ever the mechanism used for extension and retraction. Note also that pantographs are not always two-position, some designs have fairly sophisticated sensing mechanisms and fine position and pressure control.
Another typical actuation mechanism for the kind of motion you are describing is the use of pneumatics or hydraulics - you can see this in the lift arms of fire trucks, for instance, or as the actuators for garbage trucks. This prevalence of liquid / gas drives instead of electric motors is for at least a couple of reasons: Safety (electrical failures and fail-safe modes) and flexibility of power routing. It is easy to have a compressor far removed from the moving parts, and just use piping down to the actuator.
Again, there are a number of sensors involved, to ensure precise positioning with such actuators. This is either in position steps, or fully analog sensing. There are also usually independent channel end-stop sensors to account for catastrophic failures by engaging some sort of fail-safe. The positioning, either way, is via external feedback channels rather than the integrated model used in hobby servomotors.
Best Answer
Here is the drive mechanism from my beloved Butterfly Livingroom Flyer...
It is a pager motor connected to a reduction gear. By picking the size of the gears (or possibly adding additional gear stages), you can have pretty much any viable torque/power combination you want, down to single digits of mA.
If you need even a smaller actuator, Plantranco also sells the MicroAct Magnetic Actuator - 0.4g...
You could also make something similar to this yourself with some very high gauge enameled wire and a small super-magnet. This would give you lots of control of the power/torque/range-of-motion trade offs.
(Note that I have no connection to Plantranco other than I have bought more of their flyers than I'd care to admit!)
I also love Jim's suggestion of hacking a clock motor if that could work for your application. These things use impossibly small amounts of current.
Here is a product that is basically a clock motor, but good for hacking because it comes with lots of possible gear combinations, and also provides continuous rotation (the yellow metal disk acts a a flywheel), whereas clock drives usually have unneeded timing circuits and often move in a a once-per-second jerk ...
They cost about $30 on Amazon, much cheaper if you need more than about a dozen.