I have some HTML files that I want to run through sed and replace a block of text with another block. I'm doing this:

cat index.html.old | sed 's@`cat find.txt`@`cat replace.txt`@' > index.html

However, index.html remains unchanged. Is there a better way to be doing this?

That's an interesting idea, and it would probably work except for your choice of quotes. Use double quotes instead of single quotes:
The shell treats anything inside single quotes as literal text, whereas the command actually wants the shell to do command substitution inside the sed expression.

EDIT:
Just an example of what I'm getting at:

I get this:

sed: -e expression #1, char 26: Unterminated `s' command

It works for me. Here's a simple run-through:

./input_file
./find.txt
./replace.txt
Command:
You will run into problems if your find or replacement text contains special characters. For instance, since the 's' command to sed uses that '@' symbol to denote the pattern match, the replacement, and end of the sed command, the find.txt and replace.txt files can't contain '@' unless they are escaped: \@

Similarly, neither find.txt or replace.txt can have a double-quote ( " ) in them, because that will end the sed command (it matches/closes the double-quote right before s@). You can use them, but again, they need to be escaped: \"

You also need to be aware that sed will try to interpret find.txt's contents as a regular expression. That might have undesired results.

Yeah, I figured that out. I'm trying to replace some actual HTML, which I think was throwing it off. I came up with this:

The problem with this is that it literally prints `cat replace.txt` where the new HTML should go. Is there a way I can get it to put the results of the cat command there?

Not while it's in single quotes

The shell will do no interpretation at all to text within a pair of single quotes. No variable expansion, no command substitution, no file globbing, nada.

Every other way I try I get:

-bash: !--: event not found

Yeah, the exclamation mark is special to bash. You'll need to escape it too.

In case you're curious, it's the history operator (or something like that). It executes the last command that starts with the text immediately after it. So, in this case, it was looking for a command in the shell history that started with two dashes.

I guess I should have provided this before, but here's another example:

./experiment.html
./replace.txt
command:
All I did was escape the exclamation marks, and removed the backslash after the "/c"

The man page for sed makes it look like there should be one, but it shouldn't be there.

You can't have several lines of text in the regular expression to be searched without adding lines to the line buffer, and you might need to use the Hold buffer also.

You should use a form such as:
sed -f replacehtml.sed index.html.old >index.html
where replacehtml.sed is a file of sed commands.
There may be several cases to consider, such as when the pattern to be replaced is split between several lines, if two patterns to be replaced might occur on the same line, if you have a pattern on one line and the beginning of another pattern on the same line.

After you have developed your sed program, test it out on several files before process all of the files.

You can process them in a bash script like:
for htmlfile in *.html; do
sed -f changehtml.sed $htmlfile ${htmlfile%.html}.new.html
done

If what you are doing is simply replacing html files with references to those files, then a script that takes the names and enters the names into a new document may be a better option. If you use bash, consider using "printf". It is more flexible than using "echo".