I am building a z80 based 8 bit computer, and I really don't want to fry my chip. I was looking at this datasheet, but I couldn't find the fan-out specified. There are some electrical characteristics on page 30, but that's about it. In the book called "Build your own z80 computer" by Steve Ciarcia, his outputs were buffered. If I'm not mistaken, CMOS should be able to drive quite a few inputs, but I'd appreciate if someone who knows better could tell me whether or not should I buffer them. I would like to reduce the price of the whole project if possible, and pack it in a box that is as small as possible, so it would be cool if I could avoid it.
74xx245 are cheap and/or can be salvaged from computer scrap (if you are capable of desoldering) in large amounts.
Unless you are driving TTL circuitry, the reason you want a buffer is more about capacitive than DC loading.
Mind that NMOS and TTL outputs can be rather asymmetric regarding high vs low driving power, and that TTL inputs are asymmetric regarding consumption!
According to Z84c datasheet, all timings are measured at 100 pF capacitive load. Since your surrounding chips are CMOS, you shouldn't worry, as already said, about DC loading, only capacitive one. The capacitance of single IC pin is in range of 5..10 pF, so if your board has fanout less than ~10..15 IC pins per any Z80 output, here you have nothing to worry about.
But there is still some thing inherent to CMOS Z80 -- it makes very sharp signal changes so that even 20 cm of a PCB track connected to Z80 output could have significant ringing on every state change, up to the level other chips would accept that ringing as an extra signal changes.