Considering the Nikon lenses:
- AF Nikkor 14mm f/2.8D ED has a huge front glass (●₃),
- AF-S Nikkor 50mm f/1.8G has a tiny little front glass, deep inside the body (∙₁),
- AF-S VR Nikkor 105mm f/2.8G IF-ED has a tiny little front glass (∙₁),
- AF-S VR Nikkor 200mm f/2G IF-ED has a huge front glass (●₃),
- AF-S Nikkor 300mm f/2.8G ED VR II has a huge front glass (●₃),
- AF-S Nikkor 14-24mm f/2.8G ED has a large front glass (●₃),
- AF-S Nikkor 24-70mm f/2.8G ED front lens is still much larger compared to non-professional lenses of the same range (●₃),
AF-S Nikkor 70-200mm f/2.8G ED VR II has a large front glass (●₃).
AF-S DX Nikkor 18-200mm f/3.5-5.6G ED VR II front lens is much smaller than any of the three lenses above, but, well, it's a DX lens (•₂),
- AF-S VR Nikkor 70-300mm f/4.5-5.6G IF-ED front lens is small too compared to the lenses below (•₂),
- AF-S VR Nikkor 24-120mm f/3.5-5.6G IF-ED front lens is again quite small (•₂),
- AF VR Nikkor 80-400mm f/4.5-5.6D ED front lens is pretty small compared to 200mm or 300mm or the 70-200mm (•₂).
I don't see any relation between the size of the front glass and the focal length, focal range or image quality.
If we take only zoom lenses, there would be a link between the maximum aperture and the size of the glass, larger aperture requiring a larger glass. Actually, this is not true, since AF-S Nikkor 17-35mm f/2.8D IF-ED has a large maximum aperture, but a small front glass. Also, this doesn't work at all for prime lenses, where the lens with the largest aperture has the smallest front glass.
The quality of the lens doesn't seem to influence the size of the front glass neither, at least not for the prime lenses.
So what forces to make larger lenses with larger front elements?