Charles Perrault's Mother Goose Tales:
Brief introduction to Mother Goose, with links to English-language texts of the eight stories in Histoires ou contes du temps passé, avec des moralites (Histories and Tales of Long Ago, with Morals (1697), whose frontispiece showed an old woman spinning and telling stories, with a placard on the page which bore the words Contes de ma Mere l'Oye (Tales of My Mother the Goose).  These are fairy tales (not verses), most now classics. 
In addition, there are three verse-narratives published 1691, 1693, 1694.

Charles Perrault's Mother Goose Tales  with wonderful illustrations by Gustave Dore, 1867.
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Note that there is another supposed Mother Goose gravesite, as well, at St. Olaf's Church in London, England, where there is a  Burial Register plaque stating "14 September 1586 MOTHER GOOSE". This is two entries above Samuel Pepys’s burial plaque.

The Baby's Opera: A Book of Old Favorites with New Dresses by Walter Crane
          -  illustrations by Crane, 1877- included with each rhyme is its musical accompaniment.

The True Mother Goose - Songs for the Nursery, Or, Mother Goose's Melodies for Children
          -  notes and pictures by Blanche McManus, 1895

The Real  Mother Goose  -  128 rhymes; illustrated by Blanche Fisher Wright, 1916
 

Major Online Book Collections

The Gutenberg Project  has a library of over 20,000 free ebooks whose copyright has expired in the United States. This resource has not only some Mother Goose books, but other antique children's books and stories, as well as other fiction and nonfiction  From the Home page, fill in Mother Goose in the Title box and click. Currently there are six that include "Mother Goose" in their titles. Individual rhymes published as complete books can be searched for the same way. This site does not include illustrations.

Children's Books Online: the Rosetta Project  probably has the largest collection of illustrated antique books online. Here you'll find Molther Goose, and other nursery and children's rhymes and tales. There are many foreign-language versions, from French, German, Greek, Italian, Portuguese, Spanish, Turkish to Afrikaans, Hrvatski, Romano, Nederlands, Suomecki, Svenska and more. Not all entries are in all languages.  The illustrations are beatiful, high-quality, but the reading and page-looks are a bit daunting, each page needing to be enlarged, read, and unenlarged before the next page can be viewed.

The Mother Goose Pages  is an excellent site from the University of Michigan. There are rhymes, resources, and suggestions for sharing Mother Goose with children.

My Nursery Rhyme Pages  is an excellent site from Kennesaw University. There are rhymes, resources, and suggestions for activities with children.

A Land of Nursery Rhymes  is a full UK site with over 1000 nursery rhymes plus songs, riddles, puzles, and more.

Mother Goose  has 362 rhymes, games, crafts, and some "twistful tales" based on nursery rhymes.

Mama Lisa's World  goes abroad to provide some nursery songs from different countries, giving both the foreign words and the English translations, along with single-note music sounds. Site also has general Mother Goose rhymes. 

Chinese Mother Goose  shows the English-language Chinese Mother Goose rhymes collected by Isaac T. Headland in 1900. This URL takes you to a page from which you select to go on, and then to a page from which you can select from among five different formats for viewing the text. The FlipaBook version is easy to use and includes the early ilustrations, which are, interestingly,  more "real life" than "children's book" style.

The India Parenting Site  contains some 80 English-language rhymes, and smaller collections in half a dozen Indian languages. 

Mother Goose: A Scholarly Exploration  is an awesome site hosted by Rutgers University, intended for scholars and those teaching early childhood literature. The site is huge, with Mother Goose research branching out into many areas. 

Mother Goose Online  is the Rutgers University list of Mother Goose links.

Mother Goose Links  is an Amherst University site with links to other Mother Goose links.