Not really, in the earlier days they just wore one layer of clothing (a loincloth, or rather just a strip of fabric wrapped around the waist for men, and a simple dress, often not covering the breasts, for women). In later days commoners would still dress like that, while wealthier people would wear more layers of similar clothes, but more refined and complex. So, men would wear several loincloths with geometrical pleating, and the first loincloth would serve as underwear. Women would wear light see-through dresses, intricately pleated sleeves, and so on, above a simple dress that would serve as underwear. So no, nothing like modern underwear. But Cleopatra would probably dress in a Greek fashion, though I'm not sure. Anyway, Greeks didn't wear panties either.