Running Facebook application on localhost

if you use localhost:

in Facebook-->Settings-->Basic, in field "App Domains" write "localhost", then click to "+Add Platform" choose "Web Site",

it will create two fields "Mobile Site URL" and "Site URL", in "Site URL" write again "localhost".

works for me.

I wrote a tutorial about this a while ago.

The most important point is the "Site URL":

Site URL: http://localhost/app_name/

Where the folder structure is something like:

app_name
¦   index.php
¦
+---canvas
¦   ¦   index.php
¦   ¦
¦   +---css
¦           main.css
¦           reset.css
¦
+---src
        facebook.php
        fb_ca_chain_bundle.crt

EDIT:
Kavya: how does the FB server recognize my localhost even without an IP or port??

I don't think this has anything to do with Facebook, I guess since the iframe src parameter is loaded from client-side it'll treat your local URL as if you put it directly on your browser.

For example have a file on your online server with content (e.g. online.php):

<iframe src="http://localhost/test.php" width="100%" height="100%">
    <p>Not supported!</p>
</iframe>

And on your localhost root directory, have the file test.php:

<?php echo "Hello from Localhost!"; ?>

Now visit http://your_domain.com/online.php you will see your localhost file's content!

This is why realtime subscriptions and deauthorize callbacks (just to mention) won't work with localhost URLs! because Facebook will ping (send http requests) to these URLs but obviously Facebook server won't translate those URLs to yours!

You can also edit 'hosts' file and create local variation of your domain.

Example

If your real facebook application address is "example.com" you can create "localhost.example.com" (accessible only from your pc) domain in your "hosts" file pointing to "localhost" and run your local website under this domain. You can trick Facebook this way.