Hm, to give examples of games where the demo made me curious enough of a game to purchase it:
1.)Earth2150. I had a Demo from a German magazine called "CBS" and I got really fast hooked up on the game. This was one of my first games that sucked me into the world of RTS games (another one is Age of Empires). An amazing game, the demo featured the tutorial and two missions. What i liked about the game was the huge tech tree nd the customization of units. You could combine different vehicles and weapons to create your own units. The game was freaking awesome and I bought all three installments of it (Escape fromt he blue planet, the moon project, lost souls).
2.)Plants vs Zombies. Same magazine, the demo featured the first and second world (front yard day and night). After I finished it I could lust for more. The game was so freaking amazing. Simple, yes, but still I was impressed how well the game was balanced. Plants can be countered with specific Zombies, those Zombies can be countered with other plants. The artwork, the humor, i liked everything about it. It hurts really much to see how EA sliced PvsZ2 into a chash grab machine with no balance at all.
3.) Defenders Quest. There was a Demo on Newgrounds (I bet it is still there) that let's you play the first two acts and includes half of the characters of the final game. The gameplay (RPG with TD mixed) and the story were very good and I wanted more from it. I wanted to see what other characters the game has to offer. The Demo got me to purchase the full version and pre purchase the sequel when it was announced. I never regret buying it, I'm still looking from time to time into it to improve my characters.
4.) Immortal Defense. Again, Tower defense (I play quite a lot of them), like Defenders Quest you get the first two campaigns for free and can purchase the game for the rest. the game had a very refreshing approach on the genre and on story telling, mixing science-fiction with spiritual ideas. I won't get into detail but the whole point of the game is that you leave your body to become the protector of your planet in an interstellar war. The gameplay was very different in the way that your own mouse cursor represented yourself and that you attacked with it enemies. It also could create points (towers) that attacked on their own. Both, towers and cursor, benefitet in different ways from killing enemies. Also new was that cash that you collected in one level was carried over to the next level instead of having a fixed value. One of the best games ever seen in this genre, maybe even the best.