SEO tools are highly helpful in analysing a website traffic and ranking. You can use free and paid, both works perfectly. Based on my interest i have picked up the following 10 seo tools.
1) Google Analytics
2) Google Keyword Planner
3) SEM Rush
4) Ahrefs
5) Dyno Mapper
6) SEO Profiler
7) Advanced Web Ranking
8) Rank Watch
9) Woo Rank
10) Moz Rank Tracker
Personally i would love all tools but some premium tools offers discounts that time you can actually get it for economical prices.
But actually the main point of using these tools is to understand your website with more insights. It actually works like a website doctor and a diagnostic tools.