You can do this through your Google Webmaster Tools account or using a platform such as Majestic SEO, which will also identify where your links are coming from and the anchor text being used.

While you are able to track the number of backlinks you have, it is much better to be spending the time creating quality content that is going to get you more quality backlinks. If you do want to check up on backlink numbers, do it for an hour at the end of each month rather than make it a huge part of your routine.