Netflix and Safari support the HDMI output for iPads. However, Netflix (as far as I know) doesn't offer HD content for the iPad so I'm not certain how much you gain by using HDMI. In any case, you can play HD content from within Safari and it appears that any website that offers HTML5/H.264 video will work with the HDMI outputs (well, it may depend upon how the video is embedded within the webpage). The playback over the HDMI connection goes fullscreen even if the webpage restricts the original to a small window within the webpage.
Also, I'm pretty certain that StreamToMe supports video out (and AirPlay), but I haven't tried it with the HDMI connector as yet. <update>Just tried StreamToMe and it seems to work very well with the HDMI cable. I played back some MKVs, .m4v, and sampled two HD .mov and they all worked quite well.
The standard video apps from Apple also support the HDMI outputs, that includes the YouTube and Videos apps.