In idiomatic U.S. English, a common term that may apply to the situation you ask about is freeloader. Here is the entry for freeload as a verb in Merriam-Webster's Eleventh Collegiate Dictionary (2003):
freeload vi (ca. 1934) : to impose upon another's generosity or hospitality without sharing in the cost or responsibility involved : SPONGE — freeloader n
The noun sponge or sponger (used in an allied sense) likewise has no inherent element of poverty. Again from the Eleventh Collegiate:
sponge n ... 3 : one who lives on others : SPONGER [where the verb sponge, to which sponger is attached, means "to get something from or live on another by imposing on hospitality or good nature {sponged off his sister}"]
A person who doesn't suffer any serious privation but subsists by asking others (whether friends, relatives, or strangers) for money, food, lodging, etc., may well be called a freeloader or sponger.