High thread count - 300+ is definitely worth it.

As for the penchant for having thick matresses these days... when I replaced my old matress, the salesman said to buy sheets one size up. I have a double bed (it was my grandparent's) so I buy queen sized sheets. That is if I can't find deep pocket double (standard) bed sheets. And sometimes the regular pocket queen is less expensive than deep pocket double. I suppose if you have a deep pocket king you're stuck.