As a new welder, I have considered this question in some depth. I can tell you from personal experience that I have picked the slag off the end of a 7018 rod with my gloved hand while the stinger was live without feeling a thing. There are several things working together to keep you safe here.
1) Welding gloves are designed to be electrically resistant. I've read that the common heavy leather type gloves are good to 400 volts, as long as they are dry. This alone should allow you to handle the electrode safely. However, I have read that it takes relatively little moisture to significantly reduce the reistance of the leather gloves, so perhaps this shouldn't be relied upon, especially in damp or hot (sweaty) environments.
2) The voltage of the elctrode is relatively low. My stick welder operates around 26 volts, and I have heard that number said for other types of welders as well, although I wouldn't assume that all welders were that way. (For example, TIG welders use constant-current and vary voltage.) Although the welder is capable of supplying more than enough amps to (literally) fry a person, the resistance of a person's body is usually high enough to keep actual current flow to a safe, if uncomfortable, level, should said current find a path through the person's body to ground. Again: safety equipment comes into play here. If you are in bare feet on moist earth, you are going to feel that shock a lot more than if you are in heavy boots on an insulating pad. In theory, if you were on a sufficiently resistant insulating pad, you could grab the electrode's tip with your bare hand and not feel anything.
As others have pointed out, DC is less likely to be injurious than AC. I have heard various explanations as to why this is so, but the preponderance of different explanations leaves me unsure as to which of them (or all of them) is right.
3) Finally, there is the question of getting shocked when welding. Bear in mind that the place the electricity MOST wants to go is back to the transformer. So if you have a solid connection between your ground clamp and the work piece, and are in the process of welding, your chances of getting shocked are very small, since current is moving through the work piece, to the ground clamp, and back to the transformer. That is most likely to be the least-resistance path to ground, although again, I doubt I would push it by grabbing the work piece with a bare hand while standing on wet ground in bare feet or something dumb like that.
Probably the worst thing you could do, from a safety perspective, would be to touch your body with the tip of the electrode while being in contact with the work piece to which the ground clamp was connected. At that point, you have inserted yourself directly in the electrical path. Bad juju. With a little imagination, I'm sure you can come up with some scenarios where this might happen: you brush yourself with the electrode while leaning against the welding table, for example. This is why heavy clothes are important--not just to protect you from slag and sparks, but to electrically insulate your body.