Are string beans kosher for passover?

String beans fall into a category called "kitniyot".  Kitniyot is a category 
including rice, corn, and soy beans, which are not forbidden by the Torah 
during Passover, but are not eaten by Ashkenazi Jews (generally Eastern 
European) because their products can be very similar to those of "chametz".  
Chametz includes wheat, spelt, barley, oats, and rye, which are forbidden 
during passover.  However, Sephardic Jews (from the area around the 
Mediterranean) do not have a prohibition against kitniyot during Passover.  
Thus, whether string beans are permissable will depend on the background of the 
individual people.  This web page discusses kitniyot and Passover:

http://www.aish.com/holidays/passover/articles/all_about_kitniyot.asp

Good summary.

Note that other than passover, there are no non-kosher vegetables.
Also note that there are certain "kashrut" rules regarding cleaning vegetables, 
the time they were grown (Jewish "kashrut" laws declare that the certain 
patches of land must not be cultivated every 7th year. This is 
termed "Shviit"), regarding donations to charity from the sale of vegetables 
("Ma'asar"). The decision of weather a vegetable is kosher, is ultimately up to 
the consumer involved. Some are more strict than others.

See <http://www.kashrut.com/consumer/vegetables/> for more information.

According to the book "Modern Jewish Traditions" string beans are the
only legume NOT to be classified as kitniyot because they were at no
point historically mixed with flour.  (Flour was cheaper than most
other grains, legumes and sugar and was therefore mized with all three
as recently as 19th century Europe.)  Therefore most Ashkenazi
traditions do NOT prohibit the consumption of string beans on
Passover, although they do prohibit all other types of beans, corn,
rice, oats, barley and rye.

Addendum: references:
http://www.miami.com/mld/jewishstartimes/living/food/2797455.htm...and
well, lots of others, too.  Run a google search for the terms "string
beans" Kosher passover and you will end up with a lot of references on
the String Bean exception (plus a lot of Kosher for Passover recipes
involving them.)
-jl

Some modern sources feel that the customary ban on kitniyot during
Pesach should be done away with altogether, particularly in Israel.  A
page which mentions this in a long discussion of the history of the
minhag is at http://info.jpost.com/C001/Supplements/Pessah/gail.html
(Google search kitniyot+ashkenazi)

Another long discussion on the subject, at
http://www.site38.com/dickisrael/kitniot.htm , is pointedly in favor
of downplaying it, though, as the author says, it is important to main
consistency within a local community. (Found on same Google search.)
This page also claims that string beans were banned only because their
name sounds like "beans", rather than due to any botanical connection.

L'shanah haba'ah b'Yerushalayim!

String beans are absolutely kosher according to all halachic opinions.
 there is no controversy on this in the sources.  There are some who
are not well versed in Jewish law who have inadverdently promulgated
the misconception that they are kitnios probably because of they name
"bean".