A while back, while we were getting fast food, my friend commented on my usage of "can" versus "may" when asking to take my order. I said:
Can I have a .......
and my friend argued you're supposed to say
May I have a .......
Although I had never thought much about it, and at first assumed my friend was correct, I later started thinking more on it and have come to doubt this to be true. "May I" implies that what you're asking for is already known to be present and available. "Can I" implies more unsurety and is therefore technically the correct answer since there's always uncertainty that a product may or may not be physically available for taking or purchasing.
At first I didn't really care, but the debate has been drawn out now and has turned into a friendly bet of sorts. I just want to know: when in a food environment, which is technically more correct. I know this stuff can be one way or the other sometimes, but I have to know what the experts believe.
Conclusion
User Eric Nolan had a very solid arugment in favor of using can over may, and that was the "more correct" usage would depend on the role of the staff which are being asked. In a restaurant the role of the cashier or waiter is very evident, and since you don't know the availability of the item (therefore do not want to be incorrect in the event this does happen) you should use can. Where role is uncertain, may is a better choice, along with the conventional politeness factor we carry with this term compared to can, which could help in gaining permission.
User Al Maki notes: There is an argument to be made that when buying something you needn't ask whether you are able or permitted to get the item", example, "I would like". Without much thought this appears to be the overall best choice in my eyes.
Final thoughts: I believe the hamburger cat meme adds some overall weight in deciding the proper usage, as pointed out by one user's comment. Next time a fat cat looks at you while eating, simply ask yourself, would it be asking "I may haz?" or "I can haz?". The correct choice is quite clear after some deep introspection.
final final thought: why does SE not have polls? Would be cool to have this feature