My first thought is that a MOSFET is what you want. These are available with very low ON-resistances - down to 1/1000th of an ohm! They need a DC bias on the gate to turn them on.
Some MOSFETs (called "logic-level gate" types) can switch heavy currents with a gate bias voltage of 5V or less. Most are only available in SMT (surface-mount technology) packages, but a few are available in THT (through-hole technology) packages. Check out this one:
http://www.digikey.com/product-detail/en/NDP6020P/NDP6020P-ND/1055922
This is a P-channel MOSFET, which is easier to drive if you're switching a positive supply rail. You can use N-channel MOSFETs but a gate bias circuit is required. N-channel MOSFETs have lower ON-resistances than P-channel MOSFETs. (The device linked above has an ON-resistance of 0.05 ohms with 4.5V of gate bias.)
If you want a SPDT switch, you'll need two of these. And you'll need some circuitry to control them.
What voltage do you want to switch? You need to describe your application in a lot more detail.