Sure, Mir and the Shuttle were always worth a look, as they were testaments to our gradual expansion into space. These satellites are usually bright, and can be pointed out in twilight to the awe of novice skywatchers. What about the many other, seemingly anonymous satellites that slowly move across a binocular or telescope field, hovering near the brink of obscurity but made obvious by their motion? I rarely paid much attention to these, until one week around a summer Full Moon. As luck would have it, the skies were clear, and I was itching to get some observing in. I just happened across the announcement of a Web site for satellite observers, the Earth Satellite Ephemeris Service. Just enter your location on the form, select a viewing date, and bang! The service automatically prints out a list of the satellites that will be visible. The information provided includes time, celestial coordinates, speed, and an estimate of the satellite's brightness. All I have to do is manually or electronically place the position information on a star chart, look up at the right place and time, and I should see the satellite.
My first attempt at using the service met with mixed results. Out of 14 target satellites in a two-hour period, I found only six. Either the ephemeris was incorrect, my graphs were inaccurate, or the brightnesses had been overestimated. The last option proved correct in most cases, as on subsequent nights I learned to keep my binoculars at the ready. It was not uncommon for satellites to be one or two magnitudes dimmer than predicted. On the other hand, I also regularly picked up UFO's, satellites missing from the ephemeris or more likely attaining a greater brightness than predicted.
It seems that the overwhelming majority of bright satellites are rocket bodies or payloads from Soviet Cosmos missions. These missions included a large number of spy satellites with classified experiments. Other visible satellites include ROSAT, SPOT, and NOAA satellites, as well as some with cryptic numeric designations. On my third night of observing, my technique much refined, I observed 12 of 13 target satellites in a 45 minute period. Most of these were just steady, moving stars of fourth or fifth magnitude. Standouts included NOAA7, which flashed off and on as it tumbled across the sky, and 96029Ar, which was first magnitude and moved an incredible one degree every second (the average is around 0.4 degrees/second). I still haven't found out the purpose or payloads of most of "my" satellites, but I'll keep investigating.
There are quite a few bright satellites up there, but there must be many more faint ones. I remember watching a 12th magnitude dot creep across the open cluster M11 as seen in a 24 inch telescope. Also, space junk is well known as a bane to astrophotographers, who dislike the streaks of satellite trails across their images. Some people spend their time trying to figure out orbital elements for satellites, but for me the watch will be merely a fun occasion and chance to sharpen my observing and map skills. When the Moon is gone, I will retreat again to the deep sky, but if I see a satellite streak across my field of view I just might chart it and try to match it to an ephemeris.