Dear LeAnn,
You bet they do! During a lunar eclipse, the Moon's speed through the Earth's shadow is about 1 kilometer per second, which is 3600 kilometers per hour or 2280 miles per hour. This means that the period of totality for a lunar eclipse can last up to 1 hour and 42 minutes. Of course, not all lunar eclipses last that long. The actual duration of an eclipse depends on the exact path the Moon follows through the Earth's shadow. Most lunar eclipses will be much shorter in duration.
During a solar eclipse on Earth, totality can only last for a maximum of 7 and a half minutes. The Earth's rotation, coupled with the orbital motion of the Moon, causes the Moon's shadow to travel across the surface of the Earth at speeds greater than 1700 kilometers per hour (1060 miles per hour). Just as for lunar eclipses, the actual duration of totality is usually not this long. During a typical solar eclipse, the Earth-Moon distance and the alignment between the Earth, Sun, and Moon are such that totality lasts for a shorter period than the maximum possible value.