You're missing more than half of the best designer scents out there. Trust me; I'm a guy.
First, there are a huge range of classics, to the point where it's hard to know where to start. The Guerlains are a good place, though: Shalimar for a classic oriental; Mitsouko, arguably THE classic chypre nowadays; Jicky is an early classic that would be pretty much unisex or even male noways. There are many more, and many more informed Guerlainophiles to guide you here.
From Chanel - well, I'm SURE you've smelled No. 5, but it's good to revisit to refresh yourself on how this archetypal perfume smells. No. 19 is a great example of a galbanum heavy green-floral. There are so many classic Chanels I'll let others guide here, but a smell around a well-stocked Chanel counter is a fragrance education in itself.
On the subject of green florals, you must try Dior's Diorissimo, the archetypal muguet - lily-of-the-valley - fragrance. You know those '80s male powerhouses like Kouros and Patou PH? They had their female counterpart in Poison, an explosive and complex floral-oriental fragrance that remains unique.
Estee Lauder has one of the classic female orientals - Youth Dew. It's spicy oriental-amber, very heavy and old fashioned; I love wearing it. White Linen is a great example of aldehydes pushed to the max. If you can find some Private Collection Tuberose Gardenia you'll experience a gorgeous modern floral that's very true to nature.
Robert Piguet is probably not as mainstream as the line once was, but Fracas is the classic tuberose and Bandit is a classic leather chypre.
I'm not a fan of them, but you should try Thierry Mugler's Angel and Alien if you want to get to know some modern classics for those with a big sweet tooth.
Tom Ford's Black Orchid is loved and loathed by men and women alike, is readily available, and in my opinion, is still the star of the TF line.
I'm trying to stick to mainstream designer stuff, but I've barely even touched what's on offer. Go to your local perfume counters and start sniffing - it'll tell you more than any of us can tell you with words.