I've heard people say you can "just drive this from a logic pin" - but the datasheets on the SSRs don't seem to (directly) indicate this.
SSRs differ in their input characteristics. Some are built with internal current limiting resistors. These usually have an input voltage designation such as 5 volt, 12 volt, 24 volts somewhere in their part number or printed on the device. All that means is that a series resistor has been added such that you can drive if from the nominated voltage without adding your own series limiter. If you are trying to drive it directly from a device operating at 3.3V it should work better if you are sinking current, and the LED anode voltage is 5volts rather than 3.3V
Some types have no series resistance. For these you MUST add your own limiting resistance. 1.4V is the typical led forward voltage and the 20mA refers to the nominal (sometimes maximum) allowable forward current. The spec you cite means you will measure an input voltage of 1.4V if you force 20maA into the device (limited and controlled externally).
The SSRs I am looking at (for example) describe the input voltage as "1.4 volts" - and show a condition, like "If=20mA".
So - does this mean I treat it like any LED - i.e. If I am driving it at 5 volts, I would (in this case) need to put a 180 ohm resistor in series with the input? From: (5v - 1.4v) / 20mA
Exactly - and your calcs are spot on too, provided the SSR in question is one that does not include its own internal resistor.
A handy hint is that you can use a 5 volt type with pretty much any higher voltage. If you have a 5 volt SSR and want to drive it from 12 volts, just add your own series resistor externally such that the allowed maximum forward current is not exceeded.