The neatnik calendar is very nice. Others are talking about enhancements they've done and I've done my own, creating a pretty faithful JavaScript implementation with enhancements:

https://github.com/abetusk/neatocal

https://abetusk.github.io/neatocal/ (demo)

URL parameters can be used to alter behavior. Here's a highlight of some of them:

https://abetusk.github.io/neatocal/?layout=aligned-weekdays&... (weekend highlighted, aligned)

https://abetusk.github.io/neatocal/?start_month=7 (academic)

https://abetusk.github.io/neatocal/?start_month=6&n_month=6 (second half, 6 month)

https://abetusk.github.io/neatocal/?month_code=1%E6%9C%88,2%... (chinese month and day)

There's also a data file option for more complex date notes.