The Daniell cell has two active electrodes, meaning that both the copper and the zink electrodes participate in the redox reaction. However, in a lemon battery for example, the copper electrode is inert - it doesn't participate in the redox reaction. When is it possible to only have one active electrode? Is it possible to generate electricity by using two inert electrodes?
A non-chemical way to generate electricity using two inert electrodes in salt water is through magnetohydrodynamics. If the salt water moves past the electrodes in a magnetic field, it generates an electric current without consuming the electrodes or electrolyte.
This could make an interesting "magic trick" or puzzle: use a moving magnetic field, e.g. a magnet attached to a motor, in a box below a beaker filled with salt water, and insert two carbon electrodes connected to an AC current meter. Of course, make sure the motor is very quiet.
Technically you could, just place two graphite inert anode in a Zinc Sulfate electrolyte, charge the battery with about 2 volts and you will end up with a Carbon/Zinc rechargeable battery
There are many half-reactions where the electrode does not participate in the redox reaction (and no metal is deposited on the electrode, which arguably would change the electrode such that it now does participate). The prime example is the standard hydrogen electrode, where hydrogen gas is bubbled into a solution in a way that the bubbles come in contact with a platinum electrode.
Half reactions where all species are soluble
Any half reaction where a metal changes oxidation states without reaching oxidation state zero (i.e. elemental metal). Iron(II) and iron(III) would be an example, or various species involving manganese.
Half reactions involving an element that is a liquid
At least at normal pressure and room temperature, only bromine and mercury are liquids. In these cases, you would dip the platinum electrode into the liquid while also making contact with the solution containing the soluble species of the half reaction.
Half reactions where one of the species is a gas
This would include the hydrogen electrode, but also other gaseous elements like oxygen or chlorine. The hydrogen fuel cell mentioned by MaxW in the comments is an example where both electrodes are inert.