The use of っ (tsu)
This has been driving me mad ever since I learned how to read Hiragana.
がんばってくださいね is pronounced "ganbatte kudasai ne", right?
Why is there the っ (tsu) there if you don't pronounce it? What purpose does it serve?

Question

The use of っ (tsu)
This has been driving me mad ever since I learned how to read Hiragana. 
がんばってくださいね is pronounced "ganbatte kudasai ne", right? 
Why is there the っ (tsu) there if you don't pronounce it? What purpose does it serve?

Answer

large『つ』　and small『っ』

『がんばつて』----->ga n ba tsu te
『がんばって』------>ga n ba tte

『あさって(asatte) the day after tomorrow』

がんばってくださいね！

Answer

Just like everybody said, it doubles any sound that goes next. (「っか」- kka, 「っぽ」- ppo, etc.) And if there's no more kana next, it just reduces (or strenghtens?) the tone of previous sound (「えっ」- Huh?) or halt it like "..." in the middle of a word. [But that's just what I think; correct me if I'm mistaken]

Answer

It serves to double the "t" of "te", thus making it "tte". Come on, man, that wasn't hard.