How Should I Watch The Melancholy of Haruhi Suzumiya?

If I were you, I would watch it in this order:

Note: This is the same as the order listed on Wikipedia.
Note on Endless Eight: I skipped most of Endless Eight for obvious reasons. Endless Eight part 1, 6 and 8 are the episodes I would watch if I were to cut out the unnecessary episodes. Part 1 is the introduction to the loop, part 6 has one special scene which none of the others do and part 8 has the loop broken. If you can't be bothered to watch three almost similar episodes, just watch part 8.

The Melancholy of Suzumiya Haruhi Part 1
The Melancholy of Suzumiya Haruhi Part 2
The Melancholy of Suzumiya Haruhi Part 3
The Melancholy of Suzumiya Haruhi Part 4
The Melancholy of Suzumiya Haruhi Part 5
The Melancholy of Suzumiya Haruhi Part 6
The Boredom of Suzumiya Haruhi
Bamboo Leaf Rhapsody
Mysterique Sign
Remote Island Syndrome Part 1
Remote Island Syndrome Part 2
Endless Eight Part 1
Endless Eight Part 6
Endless Eight Part 8
The Sigh of Suzumiya Haruhi Part 1
The Sigh of Suzumiya Haruhi Part 2
The Sigh of Suzumiya Haruhi Part 3
The Sigh of Suzumiya Haruhi Part 4
The Sigh of Suzumiya Haruhi Part 5
The Adventures of Asashina Mikuru Episode 00
Live Alive
The Day of Sagittarius
Someday in the Rain