Oddly enough, both are correct, both are normal, and both are frequently used--both in colloquial speech and in formal writing. There is almost no difference in meaning. Of course you need to do what your teachers say, but... anyone who says you cannot use "the" is simply wrong. "Manson 'had the mystique of the ex-con, he had a good you-can-be-free metaphysical rap' — and he played the guitar." --U.S. music-oriented newspaper, Rolling Stone "Heitor Villa-Lobos ... played the guitar; consequently his writing is very idiomatic and well suited ro the guitar."--U.S. book about music. "he therefore offered the post to Ernest, who he already knew played the organ"--British novel written in the 1870s. "Wolfgang played the piano and the violin at the various churches"--Grove's Dictionary of Music and Musicians, 1910 (famous British reference book about music). I'm not sure, but I think "I play guitar" simply means I am able to play that instrument, or that I do play that instrument in a band; while "I play the guitar" carries a faint idea that you are thinking about more than one kind of instrument: "I play the banjo, and I also play the guitar."

Both are correct. I might opt to say "the" more often but I've definitely dropped the "the" too. Dropping marks for not including the "the" seems very harsh as it completely makes sense.

Thank you guys!

When we talk about musical instruments, we need to add "the" before it.

It depends entirely on the situation. If they are talking about a continuous, colloquial situation, 'I play （The)　guitar'　The 'the' is dropped and insinuated.　Or, if it is meant as a 'reply' to a question it seems correct to reply without the 'the'.