What is the best tool/method to check on the backlinks of your competitor?

[Jennifer Neon]

To keep it short and simple I will say the following tools are enough for fulfilling your purpose:
1. SEMrush
2. SEOMoz
3. ahref
4. ubersuggest SEO analyzer

I consider these to be my top choices for finding competitors backlink.

 

[Jennifer Neon]

I think SemRush is the best tool to do a competitor analysis.

Totally Agreed

 

[kyotobaths]

There are many tools are available

Google Analytic
Google Webmaster
Google Adwords