The spectrum of standard cocktails can be measured by two dimensions, popularity and difficulty. The more popular a cocktail is the more likely any bar will know what it is and serve it. Some examples of popular standard cocktails include (but not limited to): Cosmopolitan, Red Headed Slut, Apple Martini, Mojito, Amaretto Sour, etc...
Most classic cocktails are on the less popular side of the standard cocktail spectrum with a few exceptions like the Daiquiri, Margarita, and Martini.
The difficulty of a cocktail deals with what it takes to make the drink. Drinks that have a lot of ingredients, are layered, frozen, muddled, or rimmed with salt or sugar tend to be the more difficult variety. Some examples of difficult drinks include (but not limited to): Long Island Iced Tea, B-52, Frozen Daiquiri, Old Fashioned, and Sidecar.
Okay stay with me here... If you rank the popularity of a cocktail on a scale from 1 to 10 (10 being the most popular), then rank the difficulty of a cocktail on a scale from 1 to 10 (10 being the easiest), add those two numbers together, and then line them up from smallest to greatest you get the spectrum of standard cocktails.
With that said there is a time and a place for everything.
First let's discuss time.
If you are in a bar in the middle of an afternoon, you are the only patron in the bar, you can order pretty much any cocktail that is considered a standard cocktail. As the bar gets more busy the less of the standard cocktails you should order. The less popular, difficult drinks (low end of the scale) are the first to go. The most popular easy drinks (high end of the scale) are the last to go. So in a situation where the bar is four people deep waiting on drinks the order should either be right off the bar's specialty menu or the simplest of popular standard cocktails... example Vodka and Tonic.
Obviously this is a judgment call as there really isn't a documented list of standard cocktails and their rank in the spectrum. The figure below attempts to graphically depict this concept. There are many more standard cocktails than what is on the chart, but for simplicity sake only a few were pulled as an example. Also the rating of difficulty and popularity is only my opinion and should not be taken to heart. To do this right would require a rather extensive survey and the results would vary based on the regional locale. This is why you really have to judge for yourself and rationalize the cocktail order in each situation.
Next let's discuss the place.
This is a really difficult thing for a patron to judge. It really depends on the experience of the tender behind the bar.
Some places lean heavier towards their drink specialties. Bars at Mexican restaurants are a good example of this. They general specialize in Margaritas and various other tequila cocktails. These drinks are pretty much all they get orders for, so there is very few standard cocktails available.
The class of the bar and the other patrons inside the bar can also be a good clue as to what range of cocktail are available. A place with a nice wooden bar, brass rails, dimly lit lights, and a mixed age crowd will be more likely to serve up the full range of standard cocktails. Hotel and country club bars are almost always a good bet.
The last two paragraphs are highly generalized. There are exceptions, any place can have a bar chef that is grounded in the fundamental cocktails that can/will make any standard cocktail no matter how busy they are. When you find a place with a bar chef like this treasure it and tip big.
As stated above this is sometimes very difficult to judge by a patron and can lead to frustration on the part of the patron and the bartender. In a recent post Mexican Restaurant in Mandeville, LA I was disappointed with my experience. Yes the place was a Mexican restaurant but the bar is very classy and there was a mixed crowd. So, I guess I expected more... I judged wrong.
So the next time you belly up to a bar and you are thinking about ordering something not on the bar specials think about the standard cocktail spectrum. Size up the time/place and the popularity/difficulty of your cocktail and order accordingly.