Please can you advise if you have a criminal record for burglary and
possession, whether this will mean that you are denied entry to the US
on the Visa Waiver  I-94.

Hi knowlesy,

If you have a criminal record for burglary and possession, you will be
denied entry to the US under the Visa Waiver Program (VWP).


"The Visa Waiver Pilot Program (VWPP) allows aliens traveling from
certain designated countries to come to the United States as temporary
visitors for business or pleasure without having to obtain the
nonimmigrant visa normally required to enter the United States. The
program authorizes the Attorney General to waive the `B' visa
requirement for aliens traveling from countries that have qualified on
the basis of requirements set forth in section 217 of the Immigration
and Nationality Act. There are currently 29 countries participating in
the program.
(...)
To be admitted to the U.S. under the program, travelers must be a
national of, and present a passport issued by, a designated country,
plan to visit the U.S. for business or pleasure for 90 days or less,
enter the U.S. via a participating carrier (most airlines and
passenger lines, including cruise lines, are participating carriers)
or via a land border, have an onward or return ticket if traveling via
air or sea and be otherwise eligible for admission (in other words,
not be ineligible for admission because of a prior visa refusal,
criminal record, previous deportation, etc.)."

THOMAS Library of Congress: VISA WAIVER PERMANENT PROGRAM ACT
http://thomas.loc.gov/cgi-bin/cpquery/?&db_id=cp106&r_n=hr564.106&sel=TOC_23683& 


What Do I Need to Enter the United States under the VWP? 

*be a citizen of a Visa Waiver Program country; 
*have a valid passport issued by the participating country that is
valid for six months beyond your intended visit;
*have a machine-readable passport (MRP);
(...)
*have no visa ineligibilities. This means if you have been refused a
visa before, have a criminal record or are ineligible for a visa you
cannot travel on the Visa Waiver Program. You must apply for a visa to
the U.S.
---------------------------------------
When Does a Citizen of a VWP Country Need to Apply for a Visa?

You must apply for a visa under the following circumstances, if you:
*want to work or study in the United States; 
*have been refused a visa or admission to the U.S. before; 
*have a criminal record

Bureau of Consular Affairs, U.S. Department of State
http://travel.state.gov/visa/temp/without/without_1990.html


Visa Waiver Program
"Note: Members of Visa Waiver Program countries who want to work,
study or remain more than 90 days in the USA must apply for a visa
before travelling, as should those who have been previously refused a
visa, have a criminal record, or are in any way ineligible for an
unrestricted visa."

Last Minute: USA Passport/Visa Guide
http://travelguides.lastminute.com/sisp/?fx=location&loc_id=131145&sub_section=Passport/Visa


Search criteria:
"criminal record" denied entry visa waiver I-94
"criminal record" denied entry I-94
"criminal record" "Visa Waiver Program"

I hope this is helpful. If you have any questions regarding my answer
please don't hesitate to ask before rating it.

Best regards,
Rainbow