I had to grow into it, but did quickly and intentionally. I thought "amber" sounded divine, and ordered 10 or 20 samples of amber-heavy scents on eBay. When I opened the little box, the aroma wafting out at me was a little off-putting - animalic, unfamiliar, but compelling. I tried them all, and whatever had initially drawn me in bloomed enormously, and now I love amber, whether it's soft and mild or brash and surprising.
The only one I have that I'm not at home in yet is Montale's Oud Ambre, but that's probably my unfamiliarity with oud, not with amber. Of course, there are notes I can't stomach, and amber (although it's not really a single note, and so many different things are passed off as amber that you may just not have found the right one for you yet) may be one you won't ever find that you like. You might like the subtle amber in the drydown of Prada...and I believe Laura Mercier's Ambre Passion is very pleasant.