There are basically three general choices for motors:
Steppers - Can be run open loop, essentially "self encoding" for positioning, but the power/weight ratio isn't all that great, and efficient drive circuitry, particularly for high step rates, is difficult. For small motors, there are single IC drivers available from Allegro, among others.
DC Permanent Magnet - DC PM motors are by far the most common in robotics applications.
AC Motors - need a three phase inverter, probably worth looking at for a BIG robot (>500 kg)
It turns out that most small DC motors tend to have fairly high speeds: several thousand RPM is typical. On the other hand, most robotic loads require somewhat slower speeds: around 60 RPM (1 rev/second). There are DC motors that have lower shaft speeds (several hundred RPM), but they tend to be fairly large and heavy for the power output. This is because the physical size of the motor is largely determined by it's torque, and for a given power (i.e. horsepower or watts, proportional to torque * speed), lower speed motors have to have more torque. For a given current, a lower speed motor will need bigger magnets (torque is proportional to the product of current and magnetic field).
The other solution is to use some form of mechanical speed reduction: a gear train, a belt/pulley arrangement, or a lead screw. All of these have some losses involved (efficiencies go from <10% to 90%, with larger ratios being less efficient, usually), but the resulting "motor+gear train" package might be smaller, lighter, and cheaper than a motor alone, and you might be willing to take that and use the mass savings elsewhere (like for more batteries to run the less efficient motor/gear train).
You can make your own gear trains: gears are fairly cheap, but be warned that designing and building quiet running, reliable gear trains is a demanding mechanical engineering task. Alignment of the gears is critical for reliability and life. Building your own low backlash gear train is even a bigger challenge.
Belts and pulleys (and their cousins, sprocket/chains, cogs/toothed belts) are fairly easy to build, and tolerate mechanical misalignments well. They have backlash problems (unless you make the chain really, really tight, which causes other problems), and it is difficult to get more than a 5:1 reduction in one step. However, for sliding something along a track, for instance, a belt (or cable) and pulley is a great technique.
Lead screws are a convenient way to turn rotary motion into linear motion, especially with high forces. The quick and dirty approach is to use a piece of threaded rod ("all-thread") and a standard machine nut. This will have fairly high backlash and poor efficiency, but it is cheap. A better approach is to use a real ballnut and a lead screw with a suitable thread (i.e. an Acme thread). If your lead screw is thin, don't load it in compression, or it will buckle. Thrust bearings can be a bit tricky to rig up, although with the cheesy allthread approach, two nuts jammed together can make mounting that can then act on an inexpensive thrust bearing.
Buy someone else's gear box. If you can find a consumer or industrial mass produced gear box that meets your needs, use it. Typically, someone has done all the necessary life calculations, probably made a slick casting or molded part to hold the gears aligned properly, etc.
Windshield wiper motors - Clearly these are designed for long life and a reasonably harsh environment. You don't hear about people replacing wiper motors very often, so, given the millions in service, they must be fairly reliable. Someone who operates a delivery van in a rainy area may be operating these things 8 hours a day, 5 days a week, for 5 years. 10,000 hours is a pretty long life. They aren't real efficient in an electrical sense, mostly because they use a worm gear as the first reduction, and worm gears just aren't very efficient.
Door window crank motors - lots of torque (although there may be a spring helping counterbalance the weight of the window, but I wonder about the longevity. They are only going to be operated for a few seconds at a time, so I doubt the motor/gear train is designed for continuous operation (thermal issues).
Electric Drill motors