In general, what is the output voltage that an amplifier (not rail-to-rail output type) can provide,if it is supplied for example Vdd=+24V and Vee=-24V which is the maximum value I can get "for sure" from the output, can it reach +24V and -24V? in datasheets they always mention the minimum and the typical output voltage in some cases but never the maximum one. http://www.ti.com/lit/ds/symlink/opa2604.pdf
Firstly note that the opamp given has an unusually large supply voltage range, most opamps at +/-24V will only give out smoke.
Secondly. the spec you're looking for is in Table 6.5, page 5, conveniently labeled "Voltage Output". All figures in that table are for supply of +-/15V, and it guarantees an output of +/-11V (typically +/-12V) under the specified conditions.
So at +/-24V you could expect +/-20V or slightly better. (Whether it can still drive 600 ohms at these voltages is another matter, I wouldn't trust it to drive better than 1 kilohm thanks to power dissipation)
Most datasheets show the output voltage over a wider range of conditions, different load impedances, etc. but Burr-Brown (now TI) don't for this one.
The data sheets don't give the maximum output voltage because a) it's poorly defined under amplifier output driving conditions and b) very few people want to know the maximum, they are interested in the minimum it is guarranteed to drive, and the typical voltage it can drive to.
The only time you would want to know the maximum is if the amplifier was driving something that needed protection from extreme voltages. In this case, the safe and sensible thing to do is to take the rail voltages, these will not be exceeded if the amplifier is doing the driving, and into a resistive load.
Warning. If the load is inductive, or sourcing a current into the amplifier, then the output may well go beyond the rails. Typically the ESD protection on an IC will clamp any pin to a diode drop beyond the rails (a few pins on specialist ICs may be specified to be able to go beyond the rails) , but that only works up to some current, after which you can damage the diode. Check the ABS max ratings on your data sheet for the largest current you can send into a pin.
The important thing to realize is that sometimes the min and max seems reversed, but it is actually correct.
You are looking for the maximum voltage. What the manufacturer is giving you that they guarantee that maximum voltage to be 11V MINIMUM (when powered with +/- 15V). They also tell you that under the test conditions most of the chips will be able to reach 12V, but... no guarantees!
Loading matters a lot. Because they specify a bunch of parameters with 600 Ohm load, they apparently find that a normal load. Usually when you have less load, say a 10k load resistor (or circuit that acts as such), the highest achievable voltage will be higher. The problem is that the datasheet gives you no guarantees in this field. Depending on the internal structure, there is probably a fixed offset (XX Volts) and a current dependent part. The rail-to-rail opamps often have the fixed part as zero.
The OPA2604 is a weird opamp. Even though they clearly allow you to power it with +/- 24V, most of the specs are given with +/- 15V powersupply. This could be taken as a hint that they are not really intending it to be used under such conditions, but they do promise the device will still work more-or-less.
Suppose you design a circuit with +/- 20V power rails. And you've studied the datasheet and it says: max input offset voltage: +/- 5mV. So you design your circuit to allow for +/- 5mV of offset. Now, when you test your circuit... it doesn't work. Turns out the offset is 10mV! Does the chip conform to specifications? Sure it does! They only guarantee that +/- 5mV at the +/- 15V power supply voltages.
I think this is a shortcoming of the way modern datasheets are written. There really are very little guarantees when you might want to use a chip slightly outside the tested conditions. In this case almost nothing is specified for power supply voltages +/- 5V or +/- 24V.