In general, games become more difficult as you progress further, but this is not necessarily a linear progression.
If difficulty progression is slow and levels stay easy for too long, players get bored and stop playing.
If difficulty progression is fast and levels get difficult early on, some players will give up and claim the game is too hard.
The reason that players stop playing, no matter whether the game is too difficult or too easy, is because they have not been able to keep an interest in the game long enough to become invested emotionally. They've got nothing to lose by quitting early.
This means that getting the difficulty progression right in the early stages of the game is, commercially speaking, more important than getting it right later on.
When considering difficulty progression, take into account the following:
1. Player skill level
All players come to the game with a differing skill level. Good progression would cater to lesser skilled players, whilst still creating interesting challenges for more advanced players. It would be good to create challenges that would improve the lesser skilled player's abilities so that at a certain point in the game, the majority of players would all be at a similar level.
2. Difficulty spikes
I believe that difficulty should come in stages, with lulls in between. If we measure difficulty as a number from 0 to 9, where 0 is intuitive to all, and 9 is attainable for the most skilled players, instead of doing this:
game--difficulty--timeline------------>
0-1-1-1-2-2-2-3-3-3-4-4-4-5-5-5-6-6-6-7-7-7-8-8-8-9-END
I would recommend something like this:
game--difficulty--timeline------------>
0-1-0-1-2-2-1-3-2-4-2-3-3-5-4-6-3-4-5-7-6-6-4-7-8-6-8-7-9-7-6-8-END
Notice how the difficulty constantly drops down after a new challenge, allowing players to get a feel for their new skill/ability and further develop in into how they play the game.
Also notice that the most difficult part is around 90% of the way through the game. I think it is good to let players play on after the most difficult challenge and boast a little, show off their skills in the rest of the game.
All of this just my opinion of course, and I'm sure others will offer theirs too.