Here is my top 5 list and comments in no particular order of preference. Each tool has their strengths and weaknesses, but together they provide a good collection of tools for the SI/PI practitioner's tool box:
1. AtaiTec Corp. ( http://ataitec.com/home). ADK (or Advanced SI Design Kits) is a collection of SI utilities, but they also offer free tools as well. The free S-parameter viewer is one tool I use quite often to quickly plot single-ended and mixed-mode S-parameters from touchstone files. The other free tool is 2D Field Solver to compute RLGC and impedance matrices of 2D transmission lines with trapezoidal cross section. It has some limitation, but for a free tool, it is quite useful.
2. Keysight ADS. ( http://www.keysight.com/en/pc-1297113/advanced-design-system-ads?nid=-34346.0.00&cc=CA&lc=eng). A well known electronic design automation software mainly used for RF, microwave, and high speed digital applications. It is one of my favorites for frequency and time domain analysis and modeling of backplane channels. The ability to use mathematical equations to manipulate data is quite useful for S-parameter mixed mode conversions. The channel modeling tool supports latest IBIS AMI standards, and is easy to set up and use.
3. QUCS.(Quite Universal Circuit Simulator) ( http://qucs.sourceforge.net/index.html). Qucs is an integrated spice like open source circuit simulator complete with a graphical user interface (GUI). If you are familiar with Keysight ADS you will feel quite at home with this tool. It has limitations for time domain analysis involving S-parameters, i.e. it cannot handle IBIS or AMI models, but quite useful for channel model analysis in the frequency domain. DC, AC, S-parameter, noise and transient analysis is possible. Similar to Keysight ADS, the ability to use mathematical equations to manipulate data is quite useful for S-parameter mixed mode conversions.
4. Simbeor Electromagnetic Signal Integrity Software. (http://www.simberian.com/). This is an affordably priced, electromagnetic based signal integrity software. It is useful for physical design of PCB interconnects and communication links operating at multi-Gb/s speeds. A recent addition to my suite of SI tools, it provides fast synthesis of any single-ended and differential line geometries, complete with industry leading roughness models. The Via Analyzer tool provides fast synthesis of via-holes and launch geometries while the Touchstone Analyzer tool provides S-parameters plotting, quality assurance and rational macro-modeling.
5. Mentor Graphics Hyperlynx SI/PI suite. ( https://www.mentor.com/pcb/hyperlynx/). HyperLynx offers industry leading full suite of SI/PI/EMC/Thermal analysis and verification software. I use it mainly for signal and power integrity analysis of post routed PCBs. It can read in a host of 3rd party design files, including industry standard ODB++ format.