Actually, I think the common practice is to be as supportive as they can be within the limits of time and honesty. But if you are the student you can help in this. If you are intending to apply to a large number of places, let the prof know this so s/he can write a general letter that can be sent out quickly. You might even suggest things that you would like stressed in such a letter.
But if the situation comes up that you are applying to a place that you are especially interested in and which may have special requirements, let the prof know that the general letter should maybe be spiced up a bit.
If the professor is somehow connected to a university or has worked with some faculty there s/he may tailor the letter in any case, knowing what they might find interesting in your background and/or potential.
Some professors ask students to write a first draft of a letter, or even the final draft.
If you are the professor, it might be useful to ask students what they think are their most important qualities and significant accomplishments as an aid in preparing any letter. It is also good to keep a general letter on file in case you are asked again in a year or so if the student's situation is changing.