There are a couple of ways to do "geosynchronous".
The most obvious way is an circular equatorial orbit at 35,786km. As I'm sure you know, but others may not, the orbital period at that distance means that the satellite completes one full orbit in 24 hours, thus it completes a circle in the same time that the earth does, so it's always over the same spot.
There is also the concept of a Molniya orbit (https://en.wikipedia.org/wiki/Molniya_orbit), where you have a small cloud of satellites (at least 3) with extremely elliptical orbits that together can provide coverage for non-equatorial areas.
If you come up with the satellite's name or designation you found, it's probably relatively easy to determine why it is at the inclination it has. Do you remember what it was you found?
I wasn't concentrating on any specific satellite, just noticing a very noticeable trend of 24 h period orbits with inclinations between 0 and 15 degrees. They are not eccentric, so I think it rules out Molniya orbits. The trend is readily apparent if you zoom out and view the Earth in profile (see http://imgur.com/FQpTkLR). There is the obvious trend at 0 degrees and then a noticeable high density from 0-15 degrees before then trailing off.
For arbitrary examples, see Palapa 1, Insat 1A, Raduga 6.
The 0 inclination orbit must be the most sought one, hence the highest density there. Then in cases where a small compromise from 0-inclination orbit was tolerable, and considering that the second most important thing is fuel consumption, I presume that the rest of orbits may have something to do with the launching point (a lot of satellites were launched from Baikonur Cosmodrome).
The most obvious way is an circular equatorial orbit at 35,786km. As I'm sure you know, but others may not, the orbital period at that distance means that the satellite completes one full orbit in 24 hours, thus it completes a circle in the same time that the earth does, so it's always over the same spot.
There is also the concept of a Molniya orbit (https://en.wikipedia.org/wiki/Molniya_orbit), where you have a small cloud of satellites (at least 3) with extremely elliptical orbits that together can provide coverage for non-equatorial areas.
If you come up with the satellite's name or designation you found, it's probably relatively easy to determine why it is at the inclination it has. Do you remember what it was you found?