"de toute façon" is the most literal translation of anyway, but I hear alternatives used more frequently:
quand même = even so
bref = in summary
en tous cas = in any case
"It's raining but I'm going out anyway."
"Il pleut mais je sors quand même."
"My car is unreliable, but anyway, it will do the job."
"Ma voiture n'est pas fiable, mais bref, elle fera le travail."