Chirag shared good software lists, for checking backlinks of website there are tools like Opensiteexplorer in moz where you can check your backlinks,domain authority,page authority,keyword explorer etc. This is a paid tool but has 15 days free trial to begin with.
There are many tools to analyse your website ranking and backlinks of your competitor they are
- Ahrefs.
- Majestic SEO.
- Open Site explorer.
- SEO spyglass.
- Backlink Watch.
- Google Alerts.
- Link diagnosis.
Well I had to check the links for one of my competitor who is selling leather jackets with in Australia with the name of Leather Jacket Hub, after reading some blogs I got to know if we type command site: competitorname.com then we will come to know from where are they getting some signals.