Should I provide a letter of recommendation/reference to every asking student?
You don't have to provide any student with a recommendation. In fact, it can actually be a detriment to the student to have a tepid recommendation. If you find yourself unable to write anything beyond what can be confirmed by a transcript (e.g., that the student did take your class or that the student got an A in the course), then that is usually a sign that you're not someone who should be writing a recommendation letter. 

My personal method is if I know the student very well and s/he did good work, I write the letter. If I cannot recall who the student is, I ask for a one-on-one meeting to get a sense of why s/he is asking me for a letter. If there is a compelling reason that I (instead of someone else) should write the letter, then I usually agree with the caveat that it may not be a very strong letter because I'm not as familiar with their work. If there is no reason that I should write the letter over someone else, then I usually decline.