~ $ cat test
This is just a test to parse multiple links in one line of text, ala <a href="http://www.ipdb.org/machine.cgi?gid=3788&amp;puid=34561">10th Inning</a><a href="http://www.ipdb.org/machine.cgi?gid=3788&amp;puid=34561">10th Inning</a><a href="http://www.ipdb.org/machine.cgi?gid=3788&amp;puid=34561">10th Inning</a>with some trailing garbage

~ $ sed 's|<a|\'$'\n<a|g' <test | grep puid=34561 | awk 'BEGIN { FS="<|>" } ; { print $3 }'
10th Inning
10th Inning
10th Inning