This is an old thread but I was surprised nobody mentioned grep. The -A option allows specifying a number of lines to print after a search match and the -B option includes lines before a match. The following command would output 10 lines before and 10 lines after occurrences of "my search string" in the file "mylogfile.log":
grep -A 10 -B 10 "my search string" mylogfile.log
If there are multiple matches within a large file the output can rapidly get unwieldy. Two helpful options are -n which tells grep to include line numbers and --color which highlights the matched text in the output.
If there is more than file to be searched grep allows multiple files to be listed separated by spaces. Wildcards can also be used. Putting it all together:
grep -A 10 -B 10 -n --color "my search string" *.log someOtherFile.txt