A few directories send out emails, informing you of your sites' approval. Apart from this, you could also randomly check the directories to which your site has been submitted, to find your links.
There are also some commands that you can type in Google that could yield useful results:
If you want to see whether you're site appears in a particular directory, you could use the following command:
where abc.com is your website URL and xyz.com is the particular directory's URL
If you want to get a general idea as to how many links you may have received from various directories, you could enter this command:
With this command you are essentially searching for all the web pages where the word 'directory' and your website URL (abc.com) appear together, minus pages from your own site, i.e., www.abc.com
Note: Directory links do not appear instantly (could take up to 90 days) and even after they do appear, it could take a while before Google and other search engines actually find them in the directories. Only when this is done, can the links appear in Google's results.