CoD - uses a crappy routing system where everything is dynamic and based off the same URL. It would be awesome if you could do something like weather.cod.edu/forecasts/nam/latest/surface/dewp or something instead of having to use their cumbersome navigation system every time. Their product selection, sector views, and comparisons are awesome. Having fewer products for things like the HRRR are a feature in my mind, since it gets delivered blazing fast. My go-to forecasting site.
TwisterData - I like that the 240hr and 384hr runs of the GFS are smooshed together. Data seems reliable, if a little slow, compared to other sites. I can't ever recall seeing TD with old/bad data. No regional sectors is crappy, and the Skew-Ts and hodos are very minimal and borderline worthless. This isn't a horrible choice for a site to look at, but it doesn't really do anything better than any other sites.
Earl Barker - an abomination of a site, but has those hard to find charts like ESRH, LLL3, etc. Spend 4 hours digging through every nook and cranny to find what you want, bookmark and label it well, and never use anything besides those bookmarks. The only certainties in life are death, taxes, and Earl's site layout.
Haz-Wx - I understand paying for models like ECMWF, I don't understand paying for free, gridded data overlaid on Google Maps. The screenshots I've seen look really pretty, but in forecasting I like easy to find and lightweight images in minimal interfaces. I need to quickly churn through lots of products. I don't want to download Google Maps API and run a ton of scripts on a tablet in the Nebraska sandhills just to see a chart of 500mb winds.
There are other sites you should consider also. With the exception of CoD (which does a poor job at it), none of the above sites include probabilistic forecast information from the SREF, GEFS, or any storm-scale ensembles. The SPC site includes SREF and SSEO graphics, which are pretty cool and helpful. Really the future of forecasting is in ensembles and I'd love to see all sites moving towards probabilistic information. On finer and finer scales, a given forecast from a deterministic model like the NAM or GFS control member can be worthless on fine scale details. Also you would have no idea what the certainty of the forecast was, nor its dependency on forecast hour or location.
For spaghetti plots of the GFS, I'll either roll my own in IDV or use NCEP's model guidance site. It's nice for looping and seeing how the GFS converges on a solution over time, especially in regards to the jet stream and troughs/ridges:
http://mag.ncep.noaa.gov/model-guidance-model-area.php
SPC's SREF is used quite a bit by me as well:
http://www.spc.noaa.gov/exper/sref/
I personally like ensembles as well, but I haven't seen a visualization that includes something crucial - how the data is trending. If the position of a warm front keeps trending north, the mean position is kind of worthless.