Tikal was one of the earliest games we played once we started falling headlong into modern board gaming. It is designed by some of the greatest designers - Kramer and Kiesling. Even though the first few times we played Tikal we played it completely wrong, it has always been a blast, even more so now that we know how to play properly!
All of the players are working together to explore the ruins of Tikal, but while everyone is exploring the same board it is definitely not a cooperative game. Each turn you get to place a tile onto the map representing an area of the ruins. It might have a relatively unexplored temple, some artifacts, just empty space, or even a volcano! You will want to place the good tiles (Temples, Artifacts) so that you are the only one that can easily access them while using the volcanoes and other less useful tiles to block in the explorers of your opponents.
After you place your tile, you have ten action points to use during your turn. While there are other games using this mechanic, this was the first game I played with this mechanic which is another reason it has had such staying power as one of my favorite games. These points can be used to move explorers around the board, grab up artifacts, excavate temples, building camps deeper in the jungles, and lastly - securing a temple for only your group of explorers. However, securing a temple for just you will cost you five action points and likely a decent amount of explorers so you have to decide if that is a good use of your limited resources!
We do occasionally enjoy games with direct conflict - something similar to Risk. But it is the subtle back and forth that I tend to enjoy more. In Tikal there are lots of opportunities to compete with your opponents for sets of artifacts, and points from temples, and so forth. But you are never directly attacking them in the process. More important than directly competing with your opponents is using your actions and explorers efficiently to place yourself in a position to score the most points after each volcano.
With so many actions and so many action points each turn, there is an almost infinite amount of choices for you to make. However, the game is still simple enough that the number of choices never feels daunting but more like a fun puzzle to figure out on your turn.