The general rule of thumb is to always put the / at the end of the URL. Some (bad) sites even require this. When you leave it out, it basically makes the server do a little more work.
http://www.blah.com/stuff/'>http://www.blah.com/stuff/
http://www.blah.com/stuff
where stuff is a directory that contains a file: index.html
If I type the first URL, the server looks in the directory 'stuff' for a file 'index.htm[l]' (or others, depending on the server configuration)
If I type the second URL, the server first checks to see if 'stuff' is the name of a file in the top directory, it will find that it is a directory and then it looks in the directory stuff for the file 'index.htm[l]'
So, you are helping the server out a bit by telling it that stuff is a directory and that it should look in there for a default file.
Really, it's not a big deal, but it is a good habit to include the trailing /.
.htm and .html can be used interchangeably. The .htm extension comes from the limitations on file names on the old DOS systems. The .html extension was the original extension for HTML documents. Most die hard UNIX/Linux folk (including myself) prefer the .html extension.