Looking to replace the wheels on my 94 323 hatchback. There is 13" steel wheels on it right now. Would like to put aluminum wheel on it but keep the 155/80R13 tire. or equivalent in height so the speed-O will still read right.

 

Sticking with 13" alloys will be fine.

If you want to up size your rims to 14" you will need 185/60/14 tyres.
15" rims will need 195/50/15 tyres.

 

OK. Thank you.
What factory rims will fit?

 

Protege, Miata and a whole lot more.

Wheel Bolt Pattern Cross Reference Database and Conversion Guide: Mazda PROTEGE

Keep in mind that the lower the aspect ratio the more prone to flats and rim damage you get. With 185/60x14 tires you have 111mm between the tarmac and the rim. With 195/50x15 you have only 97.5 mm between tarmac and rim. If there are a lot of potholes where you drive this is an important consideration.

 

When replacing with aftermarket or off-brand OE wheels also consider the center bore of the wheels in question and compare what you need which is 54.1mm according to the chart Tan posted. It should at least be the same diameter as what you have now, but it can be bigger, just not smaller or they won't fit.
4x100mm pattern is pretty common though.
Also, when going to wider wheels and tire, back spacing and especially off-set are important. Too much off-set and you will experience bump steer, increased/accelerated tire wear and wonky steering. Wider wheels may require you pay attention to back spacing as well. That is the distance between your wheel/tire and the clearance you have with steering and suspension components behind it.
You may also run into fender clearance issues, so be careful, especially if you haven't done this before.
As far as comparable tire sizes go, what Tan said is accurate. To decide for yourself, here's a size compare calculator you can save and use to determine how far off they new tires may be.
http://www.discounttire.com/dtcs/infoTireMath.dos

 

Here's another that may help, or confuse you. Just type in what you have and what you are considering and it will calculate the differences for you: Custom rims, wheel tire packages for your ride - RIMSnTIRES.com