You may find these other threads on the subject useful:

Tuesday vs. a Tuesday
A friday
Tomorrow is a Sunday??

Thank you cycloneviv, the links are quite useful. I still think there is more to that, though. As I understand it now, many native speakers can't really give a general explanation why in a certain case they will use "a" and in another case they will omit it. Partly perhaps for those are often interchangeable, or there is just a slight and "philosophical" difference, or there is no general rule to distinguish where one should use or not an "a."

**So, let me summarize and generalize what I have so far, and **__please correct any inaccuracy__:

*What day is it? It's Monday.*** YES**

What day is it? *It's a Monday.*** YES**
(They are interchangeable, "a" giving an emphasis on the fact it's the particular day of the week.)

*I work every week from Monday through Friday.*** YES**

I work every week from a Monday through a Friday.** NO** (I can't use "a" here, because it feels wrong

Why is it wrong?)

*I work on Monday.* **YES** (Probably the next one.)

*I work on a Monday.* **YES** (I work every Monday.)

*Tomorrow is Monday*.

**YES** (The next day is a Monday.)

*Tomorrow is a Monday.* **YES** (Emphasizing the fact it will be a Monday.)

The party is on Tuesday the 18th. **YES**
*The party is on a Tuesday the 18th. ***NO** (We're talking about a particular Tuesday, not any Tuesday.)

The 17th is a Tuesday. **YES** (The 17th falls on a Tuesday.)

*The 17th is Tuesday. ***NO** (This doesn't feel right.)

The 17th is on Tuesday. **YES** (This means that the next Tuesday will be the 17th.)

*The 17th is on a Tuesday.* **YES** (Technically correct. The 17th falls on a Tuesday every month.)

*It was busy, because it was a Monday.* **YES**
*It was busy, because it was Monday.* **YES**
(They are interchangeable. The "a" only emphasizes the fact it was the particular day of the week.)