Yes, there were. In ancient Rome, at least, there were establishments akin to fast food restaurants called popinae or thermopolia. They served full meals or snacks to passerby, along with wine and hot drinks. People enjoyed them because food was served hot; hence the name thermopolium or "place where hot things are sold."

To further the comparison, there places held unsavory reputations and were seen as catering especially to a plebeian clientele. Gambling was common, and the popinae were reputed to be the haunts of drunks and postitutes. This might be upper-class prejudice, however, and the majority of the population probably enjoyed the food of these establishments.

They were often located in the large public baths or around the Forum.

Sources: I took the information from this webpage: http://www.foodtimeline.org/restaurants.html#popina but the actual citations are as follows:

"The Broad Bean and the Moray: Social Hierarchies and Food in Rome," Mireille Corbier, Food: A Culinary History from Antiquity to Present, Jean-Louis Flandrin and Massimo Montanari [Columbia University Press:New York] 1999 (p. 136)

Roman Cookery, Mark Grant [Serif:London] 1999 (p. 14)

A Taste of Ancient Rome, Iliaria Gozzini Giacosa, translated by Anna Herklotz, forward by Mary Taylor Simeti [University of Chicago Press:Chicago IL] 1992 (p. 207-209)