That depends on the airline and very much on your class of service.
In economy class, most airlines will serve beer or wine with the first meal service. Most European airlines are a little more generous than the typical US carrier and might serve a pre-dinner drink as well (depending also on time of day).
In business and first, they will generally keep serving throughout the flight although they will often taper it down over time. Flight attendants will cut you off, if they feel you had enough and/or start to misbehave.
Keep in mind that the first thing you will in the US is to clear immigration and customs. Generally you want your wits about you during that process.