Projections and transformations can be very confusing, especially if you don't do it very often. A common transformation when working with North American datasets is NAD 83 projections to WGS 84 (Latitude & Longitude). When you use the Project tool found in ArcToolbox > Data Management Tools > Projections and Transformations > Feature (or Raster) > Project, you need to specify which Geographic Transformation you need to use. Below is a guide :

First part is the name of the transformation -> Second part is the code -> Third part is the area of use (where is the data located that is being transformed).

• NAD_1983_To_WGS_1984_1 -> 1188 -> Canada, Central America, Mexico, and United States (Alaska, CONUS)
• NAD_1983_To_WGS_1984_2 -> 1251 -> United States - Alaska - Aleutians
• NAD_1983_To_WGS_1984_3 -> 1252 -> United States - Hawai'i
• NAD_1983_To_WGS_1984_4 -> 1308 -> United States - CORS ITRF94
• NAD_1983_To_WGS_1984_5 -> 1515 -> United States - CORS ITRF96
• NAD_1983_To_WGS_1984_6 -> 1696 -> Canada - Quebec
• NAD_1983_To_WGS_1984_7 -> 1697 -> Canada – Saskatchewan
• NAD_1983_To_WGS_1984_8 -> 1702 -> Canada – Alberta

The above was taken directly from a document installed with ArcGIS, it's usually found at C:\Program Files\ArcGIS\Documentation\geographic_transformations.pdf.