usually this kinda problems either stems from fuelling or ignition system. as some have mentioned it could be the plugs or leads. but another quite common culprit is the distributor rotor. i'm not sure about the gze, but the 20vs and 4eftes, which share the same rotor model, are prone to cracking near the contact point. usually will crack into a V shape. doesn't matter if you get original denso or china taiwan whatever, same thing. always crack at that point. another thing might be the contact point at the distributor cover. sometimes crap gets built up at that area, but nothing a little sanding down with sand paper cannot fix.
as for fuelling as some have mentioned as well, the most common problem is with the injectors. they've either clogged up or have gone past thier lifespan. fuel pump also could be the problem. either the wiring to the pump have started to rot or the wiring is just plain faulty. or the pump itself could be dead. the easy way do determine this to just place your hand over the cover of the fueltank cover under the rear seat and see if got any whirring sound or vibration, if got means fuel pump ok. another one is something alot of ppl overlook but can be the problem: fuel filter. this is something ppl kinda forget about. over time all the rubbish from the fuel and in the lower half of the fuel tank will start getting pumped into the engine. the crap will clog the fuel filter and eventually when the fuel filter also filled with crap, all the crap will get to the injectors.
thats all i can offer based on my newbie experience.