I must admit that I never had any interest in Gundams before the last year. I know I love giant robots, but the combined fact that Gundam series never aired in Brazil before Gundam Wing in 2000s and that this specific show failed to catch my interest. But when I saw Gundam 00 and Gundam Seed last year, I finally got interested in the series for several reasons.
The first thing who got my attention was the Gundams themselves. I have being a fan of giant robots since Macross/Robotech and Transformers, so seeing another show with cool robots fighting each other is always nice. The robots in the show aren't AIs but piloted machines, used basically as infantry units in the several wars depicted in their several shows.
The wars are the second factor that attracted me to the show. It is never a fantasy war, like the Gundams fighting some alien invasion, mystery force or because they want some legendary item. It always a 'realistic' war, with two or more countries involved in disputes over territory, resources and/or independence. And the factions involved are always human beings.
Also, it is not an evil VS good conflict. You don't have the righteous side fighting the utterly evil opponent. The show make it very clear that each side have good people and bad people, and that each side, from their own perspective, are right in their reasoning for the conflict. Some times, both sides are manipulated by a third power in the shadows, profiting somehow from the war.
The third reason I love this show is in fact its characters. They are rarely entirely evil or flawless good, they are very human, with their own reasons and worryings. Even the most devious villain may have some righteous reasons for their acts, and the goodhearted hero may make a devious act because the circumstances forced him to.
The fourth reason I love this show is the fact that, like war, no one is safe from death. A very good person can die horrible at any moment, not only people with a villainous side. Innocent civilians aren't safe from harm, even the elderly and children. It shows war as it is, a horrific conflict where no one is really safe.
There is several series in the Gundam multiverse, with several time lines and while some shows connects with previous ones, there is many unrelated ones, except by the Gundam basic design and the war theme. Therefore, they may oscillate in quality. Remember also that this show started in 1978, so animation also vary in quality.
If you are interested, there is several TV series, OVAs, movies and manga that you can use to start in the Gundam universe. I think Gundam Seed is a great place to start. You also can, like me, get interested in assembling the plastic models, which are usually great and fun to do.
Gundam is on of the greatest influence in Japanese pop culture, and it is composed of great shows overall. in my opinion, it is one of those must see shows out there.