If the head of the screw is recessed then I don't know of a way.
If it's not recessed then you could grab the head with pliers or locking pliers.
I suggest that you purchase a full set.
If you are diligent about putting the wrenches back in the case, then you will always have the right wrench.
lifehacks.stackexchange.com/users/10378/James
There aren't many possible alternates to a correct hex key.
Sometimes you can find a flat blade screwdriver that will fit corner to corner in the socket of the screw.
Some sizes will fit a Torx or other six-lobe driver (possibly requiring driving the bit into the socket with a hammer, which I've done to remove a screw with a rounded-out socket).
As noted previously, if the screw has a common socket head (as opposed to button, found, or flat head) and clearance around it you may be able to grip it with pliers or locking pliers ("Vise Grips").
Beyond that, you need a correctly sized hex key.
If you're only going to get one, I recommend a 5/32" or 4 mm, as it's easily the most common size for furniture assembly and other "some assembly required" stuff -- likely chosen because those two sizes interchange, greatly increasing the likelihood someone will have a key that fits.
You can get those that will reside on a key ring
and then you'll always have one with you.
lifehacks.stackexchange.com/users/9830/Zeiss Ikon
My Dad always says “The right tool for the right job”.
If the job is unscrewing a hex head bolt then the right tool is the appropriately sized hex key so your best option is to buy the correct tool.
However, there is one other option which will work acceptably in most cases if you’re in a real pinch.
You can find an appropriately sized bolt to fit in the head of the hex bolt and use that to turn it out.
By adding a couple of nuts to the threaded end and locking them tightly together, you can place the head of the bolt into the head of the hex bolt and then use a spanner on the nut or grips on the threads to turn the bolt which in turn will spin the hex bolt.
This is how you can use a 17mm wheel nut to remove the oversized hex head drain plug from the gearbox of a Volkswagen.
lifehacks.stackexchange.com/users/7182/Steve Matthews
Using a high-speed rotary cutter (or hacksaw) create a slot across the head of the hex bolt and remove with a flathead screwdriver.
Obviously, this damages the bolt, but it is a useful technique, particularly when the bolt will be discarded or has become stripped.
lifehacks.stackexchange.com/users/25438/Fuligo septica
In concurrence with the other answers, though there are potential substitutes for tools, there are few adequate substitutes for the correct tools.
About 12 years ago I spent $200 on a 100 piece socket/bit set and was determined to keep it complete;I've used it thousands of times
and it handled everything I've needed.
To keep it complete I frequently (sometimes several times per job if the job is long) pack all the bits back into their places to check I haven't misplaced any.
If I'd had to improvise a tool every time I'd needed one from that set, I'd have burnt 10x its purchase price in time alone!
Here ends the "get the correct tool for the job, buy wisely once" speech - this is lifehacks after all If you have a grinder and a steady hand you can grid down a larger hex key to fit the current bolt.
A snug fit that you hammer in can be beneficial too.
Try to only reshape the minimum amount of the end of the tool, because you might later need to cut the shaped bit off to restore th end of the large tool to full size/reshape again To give yourself maximum scope for multiple cut-and-reshape before the tool needs discarding, work on/cut the long stem.
If you need more leverage than the short stem can give, put a small (a few mm larger than your hex key size) ring spanner around the short stem.. Kinda like this: https://www.youtube.com/watch?v=ja7Ax45DGT8 but using a ring spanner and hex key, rather than a ring and open end spanner.
If you don't have a ring spanner, an adjustable open end spanner that can have its jaws closed around most of the length of the short stem, will work as well (maybe better)
A similar technique can be used to turn a flat bladed screwdriver into a good fit - grid the sides of the blade so that it becomes fractionally wider than the hexagon is at opposing points, then hammer the screwdriver in
so it achieves a snug fit
In other times of desperation you can weld a wing nut, bolt, piece of bar etc at a near-right angle to the head of the hex screw to be removed, then wind it out by hand.
That said, if you had a welder to hand, chances are you'd have a complete socket set to hand and wouldn't need this.
Can be handy in terms of a seized in bolt though, as the heat from welding it often makes removal easier
lifehacks.stackexchange.com/users/25171/Caius Jard
Whenever I have to deal with a hexagonal screw I never have the right key wrench. So, is there a way to manage a hexagonal screw without the corresponding key wrench?
How to unscrew a hexagonal screw without the corresponding key wrench?
lifehacks.stackexchange.com
<substitute-tool>
lifehacks.stackexchange.com/questions/19252
lifehacks.stackexchange.com/users/25626/user18894
There is no clear best way to unscrew a hexagonal screw without the corresponding key wrench, and the answer will depend as to whether the head of the screw is recessed or not. You could try simply grabbing the head with a pair of pliers or inserting a flat blade screwdriver of the appropriate size. Other possible solutions involve cutting a new slot in the screw or grinding down a larger hex key until it fits. The options are to grab the screw head with pliers, use a flat blade screwdriver, use a hex key, use a high-speed rotary cutter or hacksaw, grind down a larger hex key to fit or use a hammer.
There is no clear best way to unscrew a hexagonal screw without the corresponding key wrench, and the answer will depend as to whether the head of the screw is recessed or not. You could try simply grabbing the head with a pair of pliers or inserting a flat blade screwdriver of the appropriate size. Other possible solutions involve cutting a new slot in the screw or grinding down a larger hex key until it fits. There aren't many possible alternates to a correct hex key.  If it's not recessed then you could grab the head with pliers or locking pliers.  You can find an appropriately sized bolt to fit in the head of the hex bolt and use that to turn it out or you could use a high-speed rotary cutter (or hacksaw) create a slot across the head of the hex bolt and remove with a flathead screwdriver.  
The best option is to buy the correctly sized hex tool. However, sometimes, a flat blade screwdriver can fit corner to corner in the hex socket. Alternatively, you could cut a slot in the head of the hex bolt and remove it using a flat blade screwdriver. It is generally considered that there are few alternative tools for removing a hexagonal screw. Sometimes, a flat-blade screwdriver might fit, but otherwise, the only option is probably to cut a slot in the screw with a saw and then use a flat-blade screwdriver. However, this will damage the screw.
Grab the screw head with pliers. Use a flat blade screwdriver. Use a hex key. Use a high-speed rotary cutter or hacksaw. Grind down a larger hex key to fit or use a hammer.
If it's not recessed then you could grab the head with pliers or locking pliers.   There aren't many possible alternates to a correct hex key.   You can find an appropriately sized bolt to fit in the head of the hex bolt and use that to turn it out. You could use a high-speed rotary cutter (or hacksaw) create a slot across the head of the hex bolt and remove with a flathead screwdriver.  
It is generally agreed that there are few if any alternative tools for removing a hexagonal screw. Sometimes, a flat-blade screwdriver might fit a hexagonal socket. You could consider cutting a slot with a saw and then using a flat-blade screwdriver, although this will damage the screw.