Your statement that you NEVER heard classical music is a bit rash. If you ever watched movies, TV, or even hear commercials, you have heard SOME classical music. The very fact that you are interested in it shows that there must be a reason, likely some subliminal attraction. You can always start that way. In a different generation, people discovered Mozart piano because they watched Elvira Madigan. More recently others discovered Bach cello suites after watching Master and Commander or some such nonsense...
Some of the Western classical music is constructed so that it's naturally appealing to our brains (I presumed you live in a Western culture, sorry if I am mistaken). Mozart's easier pieces are indeed prominent among these. I personally started very young with very commonly heard things like Beethoven's 9th and 5th, initially the well known easy to follow themes and then getting deeper and deeper into them. Paganini violin concertos are easy to digest, reminds one of rock guitar virtuoso stars... Ditto for Vivaldi's Seasons, which someone else mentioned. If you like vocal elements, Carmina Burana is nice - you are also extremely likely to have heard O Fortuna around somewhere.
Uncouth as it may be regarded in pretentious classical music circles, actually starting with a book, ideally with sampler CD, on the basics of classical music, can be very powerful. More people have done it than admit it...
