Let's choose - ignoring ram for now - a W65C02 processor, a 74HC00 and a 74HCT00 for glue logic (other parts in the same families have very similar values), and your SST39SF020A. Some of this data is extrapolated; it's not directly specified for the 5v Vcc for the HC and HCT parts, for example, and neither does the 65C02 specify its output levels beyond 'CMOS'.
Looking at the first two columns: the first is the level below which the input voltage must be to guarantee a low is understood by the part; the second is the maximum guaranteed low voltage output. Every part has a low output which is lower than every other components maximum permitted low input, so there are absolutely no problems there.
The second two columns tell a different story. Here we have the minimum output level for a high, and the minimum level required to guarantee its correct input. We see that all the families except the ROM have outputs that are close to the rail, well above the voltages required by all the parts. But the ROM only outputs 2.4v... that is insufficient to drive either the processor, or normal HC logic, though it's quite happy talking to itself (naturally) or to HCT logic.
The blunt answer is: it won't work.
The more nuanced answer is: it probably will. But it might not, and if it doesn't, you're out of luck. In spite of the minima for output levels, they're the minima at particular currents; in the case of the ROM it's significantly greater than the input current of a CMOS part. You can expect, in most cases, that the output will be plenty to drive the processor's inputs directly - but you would _never_ design a production part like that. One approach would be to use an HCT buffer between the ROM's output pins and the data bus which would provide a level conversion (at the cost of a few nanoseconds' delay).
I have ignored other issues here: output rise and fall times, required input rise and fall times for example. Also absolute minimum and maximum voltages. Always read the datasheet.
Neil
(true story: at a previous employer, we had a particular logic part which was powered directly from a Vbatt rail. The battery voltage of four new alkaline cells is 6.4V, dropping with time. The part had a Vcc (max) of 7v; every other maker of the similar part offered only 6.5v or 6v. The maker of the part we specified moved their foundry to a new country and thereafter certified the part only to 6.5v... we ended up buying a couple of million of the old parts, and completely redesigning the circuit for the next generation product.)