Harvesting Energy from an Electromagnetic Generator

The Joule Thief mentioned in another answer is an excellent way to harvest the dregs of battery power. However, if surface mount components are not a problem, one can do slightly better.

Look for ultra low power energy harvesting boost converters from Linear Technologies, Texas Instruments and perhaps other manufacturers.

For instance, the TI BQ25504 can harvest energy down to 80 mV supply, as long as an initial 330 mV is available for starting the process. Typical depleted primary cell batteries will provide a higher voltage under no-load than under load, so getting that initial 330 mV at start-up is not difficult.

The standard application circuit from the datasheet is thus:

This is be pretty effective in sucking residual energy out of your depleted batteries down to nearly the last drop.

For something simpler but with less challenging requirements, the SparkFun LiPower boost converter, which uses the TPS61200 boost converter IC, can be easily modified to work down to 0.5 Volt supply power: The original designer of the LiPower board has posted a blog on how to do this modification.

The key advantage these solutions have over the joule thief is the high switching frequency used, courtesy the highly integrated design, and thus the much smaller inductor required. At the end of the day, they are all conceptually similar approaches, with a quantitative difference in execution.

A conventional current transformer will do what you want.
As Jim Dearden says, you probably do not need or want a current step up transformer as voltage will be reduced AND the device will interfere with normal circuit action.

As shown below, if you use a conventional current transformer and feed the main circuit via a single turn "winding" on the core, then you will get an output voltage at lower current. Terminate the winding with a resistor and then use the voltage across the resistor as an energy source. The single turn usually consists of a conductor passed through the core laminations. This circuit produces voltage proportional to load current - so at low currents the voltage may be too low to be useful with a regulator. Replace the regulator with an "energy harvester" if you want to use a very wide range of voltages. If you remove R_CT_LOAD and place a minimum load on the regulator output it will work at low currents but Vin may rise to high values for heavy mains load. A dynamic load scheme could be 'easily enough' devised so that Vout was acceptable under most mains-load conditions.

^{simulate this circuit – Schematic created using CircuitLab}

R_CT_Load OR a consistent minimum output load on the regulator is absolutely essential at all times. The resistor value is based on manufacturer's data for the CT used and is designed to give a target V when target current flows in the input single turn.

Note that with any current transformer, if you run it unloaded Vout can rise to very high values and may destroy the transformer or connected circuitry.