Not a need answer fast question. 
Assuming that the Taser’s barbs go into the flesh and the electrical current delivers the jolt as designed, how muscular or big does a person have to be in order to not succumb to its effects? Is there anyone on the planet right now who could withstand the current?
Edit: Oh great, typo. Would a mod please edit the thread title for me?
Considering that the taser affects your nervous system, I don’t think the size of the muscles really matters much. You can’t resist a taser with larger muscles when the taser is interfering with your ability to control those muscles. In fact, you might even be more likely to cause yourself harm due to the involuntary movement of those larger and stronger muscles.
ETA: I also fixed your typo, btw.
I don’t think it’s size related at all. Some people can maintain some control over their muscles even with thousands of volts running through them. When I was a teenager someone built a device that would produce high voltage low current output to a couple of poles. You could grab them and someone would crank up the dial, we’d hold hands and it could run through several people. Some could hang on for a long time, others would let go or collapse quickly. I’ve heard that you can train to get used to to tasers and maintain control of yourself. Certainly electricians in ye olde days would get adjusted to 120AC and just use their fingers to check for a live wire.
I think that might largely depend on the situation and path that the current is taking and kind of current and possibly how conductive a persons skin might be at a given time?
taser fixes that problem by poking through the skin.
But if skinny guy wore a think rubber suit 
Short anser - IME No.
My anecdotal experience is pretty broad. The end of my military career was in a Training Support Battalion that maintained a Non-lethal Weapons training team. I’ve easily seen more than 200 exposures, possibly over 300. I’ve voluntarily taken the ride twice.
The probes don’t actually need to enter the skin for the system to function on current models thanks to “shaped pulse technology.” (See wiki, my battalion used the X26) Along with shaping the current for supposedly better effect, the system also adjusts the voltage to maintain current in the required range (ISTR it being something like 1200 Volts being applied across the probes during a typical fired into one person application but the system can ramp up to 50k volts to overcome the higher resistance of small air gaps and extra flesh in the current path.) The typical way my unit’s trainers conducted “voluntary exposure” was with the probes replaced with alligator clips on the end of the wire that were then clipped to clothing. It wasn’t uncommon for us to run the current path through 2-3 people at a time by linking arms. Those who were through both that and probes sunk into flesh didn’t note a difference other than needing to have the probes pulled out afterwards.
Muscles along the current path are basically immobilized except for small involuntary contractions. Seeing the path hooked up in different ways (like say clipped to both feet with the upper body not in the current path) really made that clear.
In my two rides of the lightning, I described the other major effect as white noise in the nervous system. Between that and the pain it can be hard to consciously to both make a decision and then perform voluntary movement. There’s lots of voluntary movement going on though. It isn’t necessarily carefully thought out. It skews towards the type of movement we are all used to seeing when something hurts. In this case it hurts a lot and everywhere all at once.
Our non-lethal weapons instructors liked to test themselves and see if they could raise their arm and flip off the person with the taser. Mostly they could regardless of size. Remember this was not generally a first exposure for them. One of the most humorous examples of voluntary motion was a Captain I can still remember was hooked up by both feet. He spent most of the 5 second exposure talking (“I get it, You can stop. Cease fire. It’s enough!”) while clearly giving the hand and arm signal for “Cease fire” after about the first second. My scrawny 6’ 1.5" and 175ish pounds managed to deliberately raise the arm and get the middle finger out on my second exposure. (My first attempt I didn’t try anything more than just focusing on not screaming, wailing, or thrashing. 
)
There’s one advantage to actually being targeted with the system for real. The distance between the probes is shorter. That leaves more of the body potentially in control if you can fight through it. That’s not size related. Of course the big disadvantage is you are generally standing so when the pain and loss of control of core muscles kicks in you likely add falling to the ground like a sack of meat to the effects. You know what they say about being bigger and falling.
Aptly demonstrated by this unfortunate bull.
Now that is how cow tipping is possible! 
Really, the weight of a cow makes it virtually impossible to tip a cow with no aid like that, even Cecil fell for the myth (!), but told us later that while unlikely it can still be possible… But, this being the Youtube era, I would had expected already to see at least one clear example of one such act (with nigh vision cameras too).
No such luck, most of the videos I saw are about how this is a myth or telling us advise about how to possibly do such a thing or complete “FAIL” and hilarious efforts. (You would need 2 or more guys to pull it out, just by looking at the energy needed and cows do not sleep standing up).
Good info, thanks all!
Not exactly non-lethal weapons, although the company has sued the crap out of anyone who says so, sued coroners to alter results to not say so, etc. Considering tasers are occasionally lethal to pretty hefty and young human beings, I would say any signs of “immunity” is just luck of the draw as to which muscles are affected and how.