If you like the broken sword game series you will find a number of other games you are likely to like below. Some of the games are very old but still play well today.
Monkey island 1-3
The Monkey Island series is more or less the poster child for adventure games. These very good and very popular games contributed a lot to the popularity of adventure games and even though the graphics might seem a bit outdated if you play the games today you will find that the games themselves are still fun to play and compete well with modern games. The first two games in the series is the by far best games in the series. The third games is also worth playing but is not as good as the first two.
Indiana Jones 4. The Fate of Atlantis.
The fate of Atlantis is the continuation of the Indian Jones saga in a story written especially for the computer game. The fate of Atlantis is a classic adventure game that plays as well today as it did when it first game out. It is one of the truly great adventure games. The predecessor, Indiana Jones and the last crusade is also a good game that is worth playing but it is not as good as the fate of Atlantis.
Sam and Max.
Sam and max is a silly, sometimes ridiculous adventure game. The game got several sequels. The game is well worth playing if you have a goofy sense of humor but is not for those who prefer a more serious realistic adventure game.
Beneath a Steel Sky
Beneath a steel sky is an adventure game set in a dystrophic future where the world is controlled by a computer and where people live in different levels of the sky scraper city depending on their wealth and social standing. With you on you travels you have your trusty robot friend that help you solve the puzzle and mysteries that you encounter along the way. Many mysteries require you and the robot to do different things at the same time. The game has a dark undertone and an interesting twist at the end. The only critic if any against this game is that it is a bit short.
Although not a personal favorite it is game that should be on this list. Partly due to its strange humor and partly because the list really should contain at least one 3d game. Grim Fandango is an adventure game where a reaper has to solve a mystery to clear his name and prevent him from being framed. He will need to set everything right in the land of the dead.
Other adventure games worth looking include those in the space, police and kings quest series.