Everyone has his favorite PCB Design software suite, no matter how good the software is by itself these tools will help with your PCB design.
1- PCB Library Expert
This tool which is IPC approved will help you designing and generating Land Patterns (Footprints) for your components. The calculations follow IPC standards and are often updated to meet the latest standards.
You should always generate a specific footprint for the components you are using.
2- Saturn PCB Toolkit
"The Saturn PCB Toolkit is the best resource for PCB related calculations you can find.
It incorporates many features that PCB designers and engineers are in regular need of like current capacity of a PCB trace, via current, differential pairs and much more. "
- PCB Via Current Calculator per IPC-2152
- PCB Trace Width Calculator & PCB Trace Resistance Calculator per IPC-2152
- Bandwidth Calculator & Max PCB Trace Length Calculator
- Wavelength calculator
- Differential Pair Impedance Calculator
- PCB Padstack Calculator
- Mechanical Data
- Minimum PCB Conductor Spacing Chart
- PCB conductor Impedances
- Units Conversion Data
- Planar Inductor Calculator
- Power Delivery System Impedance Calculator
- Thermal Resistance Calculator
- Embedded Resistor Calculator
- Crosstalk Calculator
- Fusing Current
- Effective Dielectric Constant Calculator
This one is not free. You can try it for free but if I am not mistaken it is around 300$ to buy. This software has a lot of tools regarding Gerber Viewing and Editing, DRC and DFM and much much more. I use it to check the Gerber files generated by the EDA. I run DFM checks to make sure I didn't miss anything.
Thanks to @Geoffrey Hunter for mentioning it.
NinjaCalc is "A embedded engineering calculator toolbox for doing calculations in a breeze."
If you have any tools that help you with the PCB design please make sure to mention them.