Required precision, wire length and amount of electrical noise within the system are all considerations. There are also various levels of isolation i.e. some analog I/Os have a locally generated power supply which may or may not be isolated from general logic power or may use a separately provided supply;
Similarly, the digital signaling portion may or may not be isolated from the control bus or back-plane. Obviously, remote I/O modules communicating by Ethernet or a fiber-optic based network are isolated on the digital side and may be isolated if operating from isolated supplies.
With respect to ground referencing, in some sophisticated systems there may be separate analog and digital ground systems where the analog ground may simply be a branch of the equipotential ground bond circuit which has independent paths from other grounded items but may in some cases have EMI isolation in line. One thing to note is that logic supplies must be grounded otherwise single sided branch circuit protection is non-operative. Worse, a single fault such as insulation leakage, capacitive coupling or induction can cause the power circuit to be biased to a substantial/hazardous voltage; options include powering off of the ground bonded general logic supply or using a double isolated supply. Where some amount of leakage or induction is possible, a soft ground, e.g. grounding via a high resistance shunt is sometimes the Rx.
If one looks at the various safety standards, one can see that a conforming ground system is allowed to have a substantial impressed voltage (vis criteria for ground bond testing) so single-sided voltage mode analog signaling is only suitable for rough work. Current mode signaling is, in principle, immune to ground noise; however, a lot of current mode inputs, e.g. 4-20 mA, are actually a voltage mode input with a parallel resistor and many current mode I/O are not immune to high frequency EMI. I used the term single-ended rather than single and differential because wiring differential I/O with a ground reference or using the ground plane in circuit renders it not differential.
For high precision analog signaling - probably anything beyond 6 bit precision at <=10 V - differential signaling or a lot of statistical averaging should be used. Quite a few analog inputs either use or provide the option of averaging measurements over several power line cycles which helps to eliminate many of the EMI disturbances communicated from the power lines and line connected equipment which reduces update speed to 83 or 100 millisecs and can still be 'fooled' by unipolar disturbances (e.g. triac based speed controller); this is a common trap for the unwary who either disable PLC integration or mismatch 50 and 60 Hz equipment still expect spec sheet precision ... not! Differential signaling over twisted pairs or shielded twisted pairs with one and only one ground reference, preferably center tap, is the simplest and most reliable means of achieving high precision - and many analog I/O boast 12, 16, 20 or even 22 bit digital resolution.
STP is perhaps the only means of achieving high speed high precision analog communication. In industrial applications 75 ohm coaxial connections fare poorly without an in-line isolation transformer: it is not uncommon to find melted solder on shield connections (which is one reason to be glad that industrial cameras now use digital networks to transmit images). For reference, 12 bit precision implies >78 dB SNR, 16 bit --> >102 dB, 20 bit --> 126 dB (in broadcast audio we used to target 72 dB for AM, 90 dB for FM). Still, one finds the naive claiming to use 12 bit precision with a single ended analog signal in an industrial machine ... dream on!
Thermocouples are a special case, first because they deal in mV signals so that even the type of connectors used (to be safe, always spec low-noise connectors) and kinks in the wire can make a difference. Grounded thermocouples are usually connected to a metal jacket at or near the wire bond. Obviously, since the signal represents the thermal gradient over the entire circuit, using a single ended receiver and/or a common ground bus can be problematic. Given the extremely low circuit impedance, electrical interference is a somewhat different issue: the more common problem is that a grounded thermocouple is biased beyond the common mode voltage of the input - a generic problem for any differential / isolated analog signal (preferably leave some headroom for common mode disturbance e.g. 10 V sender --> 12 V receiver).
In the modern era, most of the problems can be chased away by using remote I/O and/or analog senders which communicate on a self-isolating digital network, especially with options like internal isolation in the remote module, and placing analog I/O modules as close to point of use as possible.
PS: in industrial control systems, don't trust 16 bit or higher analog I/O that isn't isolated (you'll never find a manufacturer that even specs a PSRR or CMRR).