Share Button coming in bellow file
app\design\frontend\rwd\default\layout\wishlist.xml
OR
app\design\frontend\your_package\your_theme\layout\wishlist.xml
Find bellow code in above file
<block type="wishlist/customer_wishlist_button" name="customer.wishlist.button.share" template="wishlist/button/share.phtml" />
after comment like this way :
<!--<block type="wishlist/customer_wishlist_button" name="customer.wishlist.button.share" template="wishlist/button/share.phtml" />-->