Do you need harnesses?
 

When you install speakers, is it just take out stock, put in new, attach to same wires, or do you need a harness to connect them to the stock wires?

depends.

some japanese car (older ones at least) already have slide on terminals that will work with the new speakers

Otherwise snip n strip the speaker wire and crimp on a new slide terminals

No you don't need a HARNESS....but when you remove your speakers you will find that mazda took the two female spade connectors and put them in a plastic plug to make it ONE piece...if you are careful you can take the too connectors out of the plastic plug and just attach them to the new speakers....if you find that too difficult, or that the stock spade connectors are not the proper size for your new speakers.....then get yourself some crimp on connectors of the right size/type and do as Hiredgoon suggested. Just snip the wires off as close as you can to the stock plug....strip the wire back....and crimp on the new connectors.

Or you can go to your local Circuit City and pay $6.99 and get some speaker harnesses so 1.)You can make sure you have your polarities right and 2.)If you ever reinstall your factory speakers you still have the factory harness there.