I've mentioned in the past that the International Space Station is easily visible to the unaided eye when it passes through the sky. That means it's not hard to get pictures of it. Unless you have pretty fancy equipment you'll only see it as a bright dot of light, but that's still pretty cool, and worth a try.
This shot of the ISS is from a webcam at the Tellus Museum of Science in Georgia, which is part of the All Sky Fireball Network. That's a collection of four cameras in the US southeast looking for bright meteors; the idea being that if one is caught by more than one camera the path can be calculated in three dimensions, and a location of any potential meteorite found.
The webcam shot of the ISS was happenstance, but inevitable; when you have a camera that looks up all the time it'll get a shot of the space station eventually! But you don't have to guess; go Heavens Above, enter your latitude and longitude (which you can get from Google Earth) and it will tell you just when interesting things will pass overhead.
With that knowledge beforehand, you can plan where to position yourself to get a picture. I've done it myself, and good shots aren't hard at all.
On March 19, 2011, Ala'a H. Jawad and his nephew were photographing Orion, and didn't notice they had something unusual until they looked at the pictures on the computer. You an see the result here: a streak left by a satellite, seen by accident. Ala'a looked it up, and discovered it was an Atlas Centaur booster launched on November 27, 1963! This was just days after JFK's assassination, and only a couple of years after the U.S. put a man in space. But that booster is still up there, along with hundreds of other pieces of orbiting stuff you can photograph.
The point is, it's not too hard to get pictures like these; you don't need a telescope. Just preparation, a camera, and a tripod. So why not give it a shot?
Images credit: Tellus Science Museum. Tip o' the lens cap to Joe Schulman and Ala'a H. Jawad; both used by permission.