Things are broken up by genre or new releases just like they used to be in video stores because it's pretty intuitive way to browse movies. "I feel like watching something funny, show me all comedies". Netflix also takes it 1 step further and tries to sort it by relevance based on previous watches.
Their interface for DVD players is quite good too. The search is smart and it only takes seconds to go from the DVD player being off to watching a stream from Netflix.
I rarely load up Netflix knowing exactly what I want to watch. I have ideas based on genre what I want and Netflix lets me browse reasonably. I've been a sub for almost as long as they've been around and I still find good stuff. The only thing that lacks is newer releases on stream but you can blame the media providers for that.
My cable provider sometimes offers free access for a month to their on demand/pay per month movie service and it's a joke. Things are listed alphabetically with 90 pages to go through or it's by genre but you're stuck going through 28 pages of alphabetical results where you see nothing but the movie title and a 1 sentence plot. It's an awful user experience.