I use crimp connectors and find them to be very reliable. Pololu has a nice assortment of male & female headers, pins, ready made cables and tools to make your own cables Pololu - Crimp Connector Housings
These connectors are generally meant to be used inside an enclosure and are not intended for exposed connections in places where the wires can be tugged by children, etc. You can buy snap-lock headers and housings that have the same type of pins and connectors, but are somewhat more secure if there is a chance that cables will be moved around.
To use one like this on the board you have, you would obviously have to remove the existing male header (which can be done pin-by-pin with needle-nosed pliers).
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