Using sed you can keep part of the pattern. Just embed it in escaped parentheses and refer to it as \1, like in the following example:
echo "<title>Download Page</title>" | sed 's/<title>\(.*\)<\/title>/\1/'
you have to carefully chose the regular expression to retrieve a unique result. In the case of the title it should be easy, but what if you have multiple html tags in the same line?
I'd suggest to use an already coded HTML parser. There are plenty of them available for free and written in different languages. Just google for them to get the idea!
Edit: just thought about a more simple sed command, just removing the unwanted part:
echo "<title>Download Page</title>" | sed 's/<\/*title>//g'