Some quick definitions: Opposition is when the Sun-Earth-planet angle is at a maximum, for planets beyond Earth; it's when the planet is opposite to the position of the Sun. The angle would be 180 degrees if all the planets' orbits were coplanar, but the orbits are all a little bit inclined with respect to each other. Opposition also happens near the date that Earth is closest to the planet within one synodic period (the time from one opposition to another). I usually think of opposition as being the best time to get photos of a planet because of the minimum distance, but although that may be true for Mars, relative proximity doesn't help you much with the giant planets. They are so far away that the relative closeness doesn't dramatically affect how big they appear. What opposition does for giant planet observers is to improve the opportunity that observers have to see them. When a planet is at opposition, it's up all night long, so you have a lot of dark sky time to observe it every night.

Conjunction is when the Sun-Earth-planet angle is at a minimum, that is, when the Sun and planet are very close to each other in the sky. Again, if the orbits were coplanar, the angle would be zero, but sometimes an outer planet passes above or below the Sun as seen from the Earth, not directly behind it, so the angle doesn’t go to zero. For one or two months around conjunction, it's impossible to observe an outer planet from Earth through conventional telescopes, and communications with spacecraft located at the planet are made difficult or impossible by the Sun's radio noise. Planetary missions plan for this by curtailing their transmission requirements during these periods.

A handy way to remember these first two terms is to remember that Earth is at the center. Opposition is when things are on opposite sides of the Earth; Conjunction is when they’re together. This may seem pre-Copernican, but that’s the point of origin of us stargazers, and therefore the origin of the terms.

Another event of interest for these planets is ring-plane crossings (usually abbreviated as "RPXs" or “RPCs”). For all these planets, the inner moons and rings orbit in (or very close to) a plane that's coincident with the planet's equator. Planetary equinoxes are defined by the Sun crossing the ring plane, just as the Sun crosses through our equator for Earth’s. Since Earth is located close to the Sun, we are usually on the same side of a planet's ring plane as the Sun is, so we see the rings illuminated most of the time. But because the orbits of the other planets and Earth have slightly different inclinations, Earth doesn't cross the ring plane on the same day that the Sun does, at equinox. For the period of time that Earth and the Sun are on different sides of the rings, Earth observers are treated to a very thin view of the shadowed side of the rings. In some years, the combination of Earth and planet's motions in their orbits means that Earth crosses the ring plane a total of three times around each equinox.

The synodic period of two orbiting bodies – in our case, the Earth and an outer planet – can be defined as the time between oppositions (or conjunctions). In other words, the time required for the two bodies to “line up” and return to the same relative orientation. Since the outer planets move much more slowly around the Sun than the Earth, the synodic period between the Earth and each outer planet is slightly more than one Earth year (and is of course different for each outer planet, as they move at different speeds). The Earth makes an orbit around the Sun in one year, but must then “catch up” to the planet as it has traveled in its own orbit.

I'll start with the slowest-moving planet and move inward.