You typically need 25,000 miles for a domestic round-trip ticket. If the ticket costs less than $250, you're probably better off paying cash.
Airlines push redeeming miles online and will charge $5 to $15 to speak to a person. But it may be worth it: the airline representative has access to additional inventory on partner airlines.
Your miles stretch further on international flights, which typically require 40,000 to 60,000 miles or more depending on the destination. You want to aim to get $2 worth of airfare for every 100 miles. In other words, for a $1,200 flight to Paris, you'd be getting your money's worth using 60,000 miles.