Lufthansa and United have round-trip flights from Newark/New York (EWR) to Munich (MUC) for $598, NONSTOP. Flights October to February. Extended weekends available.
Note: Some small OTAs on Skyscanner have this for about $578. If you plan on booking there, beware of any site that charges a fee to cancel a ticket within the 24-hour “free” period. Use unknown booking sites at your own risk.
Lufthansa “Light Fares” allow for a carry-on bag (17.6-lbs @ 21.6 x 15.7 x 9 inches) and also a very small personal item such as a laptop bag (11.8 x 15.7 x 3.9 inches). The weight limit will probably be the limiting factor for those of you who wish to avoid bag fees. Prioritizing heavier items in your “personal item” may be a good way to lighten your carry-on bag. You can avoid seat selection fees by accepting the randomly assigned seat at the gate.