Also, playing by ear is usually not playing the melody. It is most often supporting the melody with a series of chord progressions.
I have played I guess professionally (at least I have been paid) for a bit over a year, and I am just now getting to the point where I am not playing the melody but letting the choir sing that while I play supporting chords.
It just takes some time.
Be prayerful and patient and persistent, and it will come.
Be Blessed,
BBoy
Man, that's a whole other level of music right there: accompaniment
You're right, BBoy!
After playing the melody on the top, with the chords underneath for years, it took quite some adjustment to just play the chords while the singers carried the melody. In fact, I'm still working at it, I guess after playing that way for so many years, it's almost automatic. 
U said it, T-Block! "Accompaniment" ... That's my desire, what I'm working to be excellent in. 
That's how the true pros play. Listen to a good recording and you'll hear that the the Keyboard player isn't following the exact melody of the song.
It's only recently that I REALLY began to try and incorporate this.
A GREAT song to listen to is Sovereign God by Maurette Brown Clark. The keyboard player follows the melody at times, and sometimes leaves the melody...all with GREAT taste.
The are a few keys to doing this:
You have to KNOW the song. If you don't really know the song too well, you're more likely to get lost if you leave that melody.
You have to have the taste to know when you can abandon the melody and when you have to come back and support it.
You have to maintain the integrity of the song. You can't leave the melody to play abstract chords that will confuse the lead singer, choir, and/or congregation.
