Can this comparator input exceed its supply voltage?
Can I use this comparator safely when it is powered by 12V and the input to its inverting input is 24V?


Short answer: 

Yes!!!
This comparator acts differently than many as regards allowable Vin voltages.
As long as one input is in the 0V to (Vcc-2V) range then the other input may be anywhere in the 0V to 36V range, without damage and with correct operation. This applies for any Vcc value from 2 to 36V.

Because:

There are limitations on what happens when one or both inputs exceed Vcommon-mode - see below. 

In Table 2 on page 4/19 it states -
Vicm: Common mode input voltage range for Tmin ≤ Tamb ≤ Tmax 0 to VCC+ -1.5
(or Vcc -2 in another row).
A look at the data sheets from 6 manufacturers shows that:  

At least one input must be within the Vicm range of 0V to Vcc - 2V *
The other input may be above Vcc - as much as +36V in some versions. 


*(For full temperature operation. Vcc-1.5V at 25C)


________________

The TI data sheet  lists the conditions most clearly:

8.2.2.1 Input Voltage Range
When choosing the input voltage range, the input common mode voltage range (VICR) must be taken in to account. If temperature operation is above or below 25°C the VICR can range from 0 V to VCC– 2.0 V. This limits the input voltage range to as high as VCC– 2.0 V and as low as 0 V. Operation outside of this range can yield
incorrect comparisons. 

Below is a list of input voltage situation and their outcomes:  



When both IN- and IN+ are both within the common-mode range:
(a) If IN- is higher than IN+ and the offset voltage, the output is low and the output transistor is sinking
current
(b) If IN- is lower than IN+ and the offset voltage, the output is high impedance and the output transistor is not conducting  
When IN- is higher than common-mode and IN+ is within common-mode, the output is low and the output transistor is sinking current    
When IN+ is higher than common-mode and IN- is within common-mode, the output is high impedance and the output transistor is not conducting  
When IN- and IN+ are both higher than common-mode, the output is low and the output transistor is sinking current  





The Diodes Inc data sheet appears the most generally useful.
(MB: Diodes Inc often make better than most spec products so be wary if using their data sheets for other brands. This noted, they can be very useful).

On page 5 note 13 they say:
"13. The input common-mode voltage of either input signal voltage should not be allowed to go negative by more than 0.3V (@ +25°C). The upper end of the common-mode voltage range is VCC -1.5V (@ +25°C), but either or both inputs can go to +36V without damage, independent of the magnitude of VCC"

Note that if both inputs are above Vcmr the output will be low (according to the TI notes above.)

______________ 

ONSEMI datasheet
ROHM data sheet
ST data sheet
Fairchild data sheet is now shared with ONSEMI 



Notes:

(1) This is based on a comment I made to to Andrew and is worth noting.

They seem to have a "different to usual" interpretation of what 'common mode voltage' means. After looking at data sheets from 6 manufacturers I think the TI summary in my answer above probably best states what happens.   

ONE input must be in the 0 - (Vcc-2) range** BUT the other can be 0 - 36V without damage AND with correct operation!
Overall this is a very unusual interpretation of terms and mode of  operation.   

Note that Iin can be very large, unlike usual devices.   


**
Diodes inc say lower Vin limit is -0.3V
Vcc-2 is for full temperature range.
Vcc-1.5 at 25C.


(2) Based on a comment that I made to Curd

I looked at 6 manufacturer's data sheets in order to elucidate [tm] what they appear to be saying.
These indicate that this device has an unusually accommodating spec and, if ONE input is in the 0 - (Vcc-2V) range, then regardless of the value of Vcc*** it will allow the OTHER input to cover the 0-36V range without damage and with correct operation.


***-
Vcc allowed = 2-36V.