What is the most common procedure when options/futures/forwards are held until expiry? Will the underlying asset be delivered in a physical way or will the value of the derivative be exchanged as a cash amount? Are there differences between stocks, commodities or other securities?
I'll address the equity/index options aspect of this.
If an option is one cent or more ITM at expiration, the Option Clearing Corp (OCC) will automatically exercise your options whether they are long or short. This is called Exercise by Exception.
For American style equity/ETF options, you will end up with a position in the underlying (long or short). European style options (most indexes) are cash settled.
If you are long the option, you can designate to the OCC via your broker that your options are not auto exercised at expiration. This would make sense if they are ITM by pennies and your commission to close the position exceeds the ITM amount.