Keyword Research Tools
I use Ahrefs for exporting lots of keywords, and they tend to have slightly more data than SEMrush, however using both is always best.
I use keyword grouper to manage large keyword lists and find the common themes / user intentions between them. It’s invaluable.
Tools for Finding Links
I use Ahrefs to find backlinks, as their index seems to find more links, and their updated DR is much better at ignoring spam links.
Screaming Frog is a great way to analyse the technical issues on a website, helping to identify broken links, redirects, canonicals, and many other technical errors.
Google Webmaster Tools is an invaluable asset when auditing a website, as it provides lots of information that you can’t get anywhere else such as crawl rates.
Google Analytics helps to analyse traffic data, find problem pages, and track organic, social and referral traffic stats over time.
The Panguin tool lets you overlay Google update points over your analyitc stats to help check if your website has been penalised.
On Page Optimisation
I use SERP preview tools to help monitor the length of snippets and make sure they look good before publishing new page updates.
Photoshop is very useful to create images for pages, allowing for text overlays and other effects that improve your conversions.
Tracking & Monitoring
I use Pro Rank Tracker as part of my daily site checkups, monitoring where projects are ranking in Google across all countries.
Uptime Robot has been very useful to make sure all websites are up and running. It can check for 404 errors and domain expiration notices.