Maximum current for a single-core cable?
Theoretically - for 700mA you should use AWG 23 wire. You can use this table for choosing wires.

AWG 23 is 0.57404mm core diameter (or 0.0226 inch core diameter).

Practically - if wire is short (few cm/inches) - you can use AWG24 or AWG25 wire and there will be no damage at all. Even thinner wire probably could survive 700mA without damage.

Note, that wire current ratings are usually determined by voltage drop/resistance. This is not maximum current without damage.

You should worry more about wire&lt;->breadboard connection resistance. 

Many breadboards on the market are poor quality and 700mA current may cause some voltage drop on connection between wire and breadboard conductive part. For relatively high currents (>500mA) I'm using double wires sometimes - to make sure that connection is good enough.