I replaced my faucet supply line but it's still leaking. Any ideas?
These fittings seal by a soft elastomer seal in the hose fitting to a smooth mating surface on the faucet fitting. I would just keep tightening until the leak stops.

If you cannot get it to stop by tightening, you could cut off the fitting on the faucet  and put on a new fitting (compression or sweat on). Is the mating surface damaged? Are the threads on the faucet fitting damaged (e.g., from prior cross threading) so that the mating surface is not being pressed square onto the seal?

If you can see or feel a groove in the sealing surface of the faucet fitting, you could try to restore the surface by filing or sanding. If it is a deep crack, then you could try to fill it with super glue or other sealer, but probably this wouldn't work. 

You could get an adapter which you could thread onto the existing faucet fitting (with pipe dope or tape) and which would have undamaged threads and sealing surface and to which the supply hose would make a leak free seal. This might require two pieces--a "nipple" and an adapter which screws into or onto the nipple and has the correct male ending for the supply hose to attach to. The pipe thread connections on each end of the nipple would require sealing with pipe dope or tape, but not the final connection of the supply hose.

EDIT


  I'm really baffled on this one. I noticed the male >threads are not completely in the round (they have flat >sides), but there is nothing unique about the supply line >that was removed. No sign of Teflon tape, and I didn't >use any.


AFIK the presence of flat sides means that these threads could never seal and are only "clamping" threads so my statement above about putting on an adapter w or w/o a nipple wouldn't work. Only round threads can seal.