Parks and gardens (15)
http://www.worldheritagesite.org/categories/category40.html

Wilhelmshöhe
Botanical garden Padua
Suzhou
Shalamar
Wörlitz
Kromeriz
Kew
Chengde
Muskauer Park
Par force
Persian Garden
Potsdam
Singapore Botanic Garden
Studley
Villa d'Este

My selection:

Suzhou
Shalamar
Kew
Chengde
Persian Garden
Potsdam
Singapore Botanic Garden
Studley??
Villa d'Este

My selection:
Potsdam

Others are covered already in other WHS I have or will select

Wilhelmshöhe - N
Botanical garden Padua - N
Suzhou - Y - representative of Chinese gardening
Shalamar -Y - for Mughal gardening
Wörlitz - N
Kromeriz - N
Kew - N - go for Singapore
Chengde - Y - but not for the garden it itself, but rather for the architecture
Muskauer Park - N
Par force - N - niche topic
Persian Garden - Y - collection of representative sites of Persian gardening
Potsdam - N -other sites seem more relevant
Singapore Botanic Garden - Y - representing botanical gardens.
Studley - N - would go for Blenheim palace (as per discussion on palaces)
Villa d'Este - N

In general, I'm not a fan of pure garden sites; for the European sites, the palaces usually include gardens as well, so I don't see a need to include many (or any) of the European pure garden sites.

My selection

Suzhou
Persian Garden

Just to put forward the case for Kew, its real value isn't that it is a good version of an English garden, though it does have some of those qualities. It's real value is for the scientific work that has been pioneered and is still conducted there. It has the largest collection of living plants in the world.
Architecturally it is pretty important for its pioneering of iron frame building techniques as well. The value of Kew is beyond its aesthetics, if you were wanting an example of an English garden Studley is the better version or Blenheim, but I can't in good conscience promote either of them as amongst the 400 best sites on earth.

I feel this a bit strange. I think Kew, Singapore and Padua should not be in this group as the idea of botanic garden is different from other landscape garden.

My selections:

Suzhou
Kew
Persian Garden

Persian Garden - iconic serial property
Suzhou - superb example of Chinese garden design
Potsdam - one of the finest landscape gardens/parks in Europe?

I really enjoy visiting gardens when traveling, but I've only been to three gardens on this list, so I guess I have some new reasons to travel! I think I'll have to take Durian's approach and organize my selections according to landscape gardens and botanic gardens.

Landscape Gardens:
1. Suzhou -- as winterkjm states, this is the epitome of classical Chinese garden design
2. Persian Garden -- great variety of Persian gardens representing different climates and timeperiods
3. Villa d'Este -- beautiful mixture of water and architecture that influenced other European gardens; I'm not sure I'd be able to keep this site in Top 200 with Versailles and St. Petersburg in the mix, but I'll at least pick it here

Botanic Gardens:
1. Kew Garden -- extensive collection of over 30,000 different kinds of plants, and conducts scientific research; also displays different approaches to landscaping, including portions designed by Capability Brown, perhaps England's greatest landscape architect
2. Singapore Botanic Garden -- tropical colonial botanic garden, with research into tropical botany and horticulture; also played a significant role in establishing rubber plantations in Southeast Asia

Time for finalizing here I guess. Bold are Yes, Italic are Maybe.

Wilhelmshöhe
Botanical garden Padua
Suzhou - epitome of classical Chinese garden design
Shalamar - for Mughal gardening
Wörlitz
Kromeriz
Kew - for its pioneering scientific work & has the largest collection of living plants in the world.
Chengde
Muskauer Park
Par force
Persian Garden - great variety of Persian gardens representing different climates and timeperiods
Potsdam - one of the finest landscape gardens/parks in Europe
Singapore Botanic Garden - tropical colonial botanic garden, with research into tropical botany and horticulture
Studley
Villa d'Este - beautiful mixture of water and architecture that influenced other European gardens

Bring Chengde over to another category (more renowned for its buildings than its gardens)

I also add my support to Villa d'Este

This does not affect the latest summary.