I have cycled a bit around the New Forest, but I fear I can only echo others viewpoints. Whilst the New Forest is undoubtedly picturesque, with lots of nice wild horses and suchlike, you are only permitted to cycle on a limited number of off-road routes. These routes tend to be quite dull gravel tracks. You are unfortunately not allowed to deviate from these tracks, or you risk a fine if caught by a forrestry commisioner. This is a shame, since it would be a whole lot more fun. So, nice for a leisurely picturesque ride, but not for anything interesting off-road. I personally think it's better for road cycling, since the roads tend to be fairly quiet and good quality, and the scenery is lovely.
This is the fun-sapping cycle code:
http://www.forestry.gov.uk/pdf/new-forest-cycle-code.pdf/$FILE/new-forest-cycle-code.pdf
Here is a map of off-road cycle routes:
http://www3.hants.gov.uk/newforestmap-2.pdf
