The Living Standards Measurement Study is ongoing as of 2012. The actual number of LSMS can be difficult to determine as a number of similar surveys have been conducted under the LSMS name, and the degree of World Bank involvement is not always clear from the documentation. LSMS listed below are listed on the World Bank LSMS Web site.
LSMS in general are living conditions surveys that provide data for conducting assessments of poverty. Most are nationally-representative, but some are subnational. The stated objective of the LSMS program is to improve the type and quality of household data collected in developing countries and to increase usage of those data for policy decision making. While not all LSMS are the same, many include anthropometric measurements, health status, fertility, and education in addition to employment, income and household expenditure sections. Many of the LSMS also include a community questionnaire to assess available community services and infrastructure, including health services.
Another survey project of interest implemented by the LSMS team is the Living Standards Measurement Study - Integrated Surveys on Agriculture (LSMS-ISA) series. LSMS-ISA surveys are nationally representative household panel surveys with a focus on agriculture.
For more information on the LSMS program, particularly in the early years, refer to "A guide to living standards measurement study surveys and their data sets" by Margaret E. Grosh and Paul Glewwe, available from the World Bank Web site.
If you are looking for LSMS-type data, depending on your interest, you might search for household budget and income and expenditure data, data that cover health status and disability, or personal health expenditure data.