Two sites that have horse racing results are Equibase and Daily Racing Form. Both sites have charts that list the day's races divided by track, as well as previous races.
Equibase has detailed files of each race's results that can be found by clicking the races from the main chart. The result information also includes a written overview of what happened during the race.
Daily Racing Form has each race listed in the chart hyperlinked to a page of detailed race results. Information provided on these pages includes horse name, jockey name and times. Weather information is also included in the details.