Would like

I'm not convinced that a difference in certainty is the best way to distinguish between would like and hope.

I hope I will followed by a verb that represents some action that we have some control over is not particularly idiomatic.  We don't hope for things that we are going to do, or can decide to do, as in *I hope I will go shopping today.  Thus, I hope I will learn English does not strike me as completely idiomatic as an isolated sentence.  (There may be contexts in which it makes more sense, however.)

On the other hand, we use would like in that situation:  I would like to go shopping today.  The meaning is close to I hope to go shopping today.  I would like to suggests that the action (e.g., going shopping) would please me; I hope to suggests that I have planned the action, and that I will perform the action if nothing else interferes with my plan.

CJ

I hope you pass the exam is more usual.
I hope you will pass the exam is less usual.
There is no difference in certainty that I can detect.  None at all.
Instead, the version with will simply emphasizes the futurity, which is not at all necessary, since the form without will (i.e., the present tense) is regularly used to indicate futurity anyway.
______

I hope I will and I hope to do not mean exactly the same thing.  They can't be interchanged.

I hope I will  is not used with an action that the speaker is going to perform.
It is more often associated with a state of affairs that the speaker hopes will come about.

I hope to can be used with an action that the speaker has planned to perform.
It is less often associated with a state of affairs that the speaker hopes will come about.
_________

Idiomatic uses:

With states and with things that happen to me and with impressions others have of me:

I hope I will be able to attend the lecture on Monday.
I hope I will not have to attend the lecture on Monday.
I hope I will enjoy the movie as much as you say I will.
I hope I will be offered a good job.
I hope I will not seem too aggressive by asking that question.
I hope I will not run into a lot of problems while finishing this project.
I hope I will receive the award.
I hope I will look handsome on stage.
I hope I will be chosen for the leading role.
I hope I will live to a ripe old age.

With actions I have planned and actions I envision doing with satisfaction:

I hope to meet the mayor at the next city assembly meeting.
I hope to complete my studies by June of 2009.
I hope to make a decision by Thursday.
I hope to get a good job.
I hope to attend the lecture on Monday.
I hope to visit many museums on my trip to Europe.
I hope to make many new friends at the new school.
I hope to find the gift that is exactly right for my sister.
I hope to finish my chores before noon so I can go to a movie later.
I hope to live to a ripe old age.

Note that there are cases where both expressions can be used (... live to a ripe old age), but the focus of the meaning is different.  I hope I will suggests lack of control over what happens to me; I hope to suggests that I am taking measures to ensure that the desired outcome occurs.

CJ