The Internet Scrabble Club (ISC) is the best place to play Scrabble online. You can compete against anyone from beginners to world-class players, and there is a nice rating system so it is easy to find competitive games no matter how good you are.
My username on ISC is jdscheff
. If you want to play me, it's probably best to send me a message somewhere and pick a time, because I usually only go on to play a random game every few weeks or so... my skills are slowly atrophying, I know. This is evidenced by my rating of 1132 (as of January 2017), which is well below my peak of 1261.