First off, when we are talking about Netflix we should consider why it is that it is so dominant. The opinions will vary, but I'll present my analysis. Hands down, Netflix has the largest selection of streaming movies, but that is where its superiority ends. Though there are many services, most are either too narrow, too expensive, or lack content; thus I will not cover them since we are looking for a replacement to Netflix, and the source of its strength boils down to content and price.
Hulu (esp. with its Plus subscription) absolutely dominates over Netflix in terms of selection for television programming. A nice addition that I appreciate is its Hulu Desktop application. Not all content available on its website is yet available for its desktop application, however it is elegant and works well. Best of all, Hulu Desktop has a native Linux version distributed in .rpm and .deb! The .rpm works well on openSUSE, only requiring a manual edit of its configuration file to let it know where the flash browser plugin is located. Needless to say, the desktop application is a serious advantage over Netflix regardless of what platform you use. This is my subscription service of choice thanks to its large library, and its embracing of Linux with its very nice desktop application.
A lot of feedback has mentioned Amazon Streaming. I did not include this since it is primarilly a per-title rental service. Though they do have a subscription included streaming package, its content has never impressed me. I had some issues with their playback as well, as have other people I know. If the performance is improved then I would certainly list it as the number one source for movies to rent since it has very large volume of titles and high quality content. It however cannot beat Hulu for performance and value at this time. The playback glitches were a sever issue to me, especially if I'm going to be paying per title what would amount to a significant percentage of the price of Hulu Plus.