In defence of Kekulé structures
The real answer is, in my view, much more nuanced than ron's answer would have one believe. I sincerely think it is too simplistic to just say that it is "wrong".
To understand what I mean, we need to look at the concept of a resonance hybrid, which is a weighted average of several different resonance contributors. Molecules, of course, do not exist as individual resonance forms (not even fleetingly); they exist solely as the hybrid. We already understand that the most accurate depiction of benzene is one which comprises two major resonance contributors, 1a and 1b:
One could argue that the only correct depiction of benzene is the resonance hybrid 1, where each pair of adjacent carbons is connected by 1.5 bonds, and indeed this position has already been argued. But benzene is not the only molecule in which resonance is crucial. Take an amide, for example: we know that the charge-separated resonance form is important to understanding (amongst others) the rigidity of the peptide bond, as well as its resistance towards hydrolysis.
Of course, here the C–O bond order is probably more than 1.5, and the C–N bond order is probably less than 1.5, but I don't have any other fancy ways of depicting non-integer bond orders, so we have to make do with this. According to the same logic as before, the only correct way of depicting the amide is the resonance hybrid 2, and using the individual resonance form 2a must be "wrong". However, it appears that the vast majority of organic chemists have no qualms about depicting amides in that form.
The same can be said of practically any other molecule, like butadiene, which is arguably even worse:
Are we not being inconsistent, then, if we claim that the Kekulé structure of benzene – i.e. one of two resonance forms of benzene – is "wrong"?
Part of the answer to this paradox is that not all resonance structures are created equal. It is obvious that in benzene, the resonance forms 1a and 1b make an equal contribution to the resonance hybrid 1. Therefore, by choosing to solely depict benzene as 1a, we are effectively throwing away 50% of the information. On the other hand, the resonance form 2a is a larger contributor than 2b to the resonance hybrid; so, by choosing to solely depict the amide as 2a, we do not discard quite as much information.
However, it still leaves us with the uncomfortable question of where we should draw the line when it comes to the supposedly "wrong" practice of using resonance forms to represent molecules. Any threshold that we come up with, naturally, can only be completely arbitrary: you could draw up an arbitrary list of what is "permissible" and what is "wrong", but you would be doing it until the cows came home.
A much healthier way of resolving this contradiction, and one that the vast majority of chemists have already adopted, is to realise that our Lewis structure depictions are always going to be approximations to the truth. With this in mind, we can comfortably choose to use one resonance structure – the Kekulé structure, for example – and trust in the reader to understand that, unless stated otherwise, we are not referring specifically to this resonance form, but rather to the actual molecule, which exists as a resonance hybrid. And naturally, we should stick to the dominant resonance form as our default depiction of the molecule: hence for benzene we could use either 1a or 1b, but for the amide we should use 2a, not 2b.
Regarding benzene in particular, I guarantee you that the "circle in hexagon" depiction does not exist in organic chemistry beyond introductory textbooks which try to teach you that the Kekulé structure is "wrong". It is virtually impossible to find the "circle in hexagon" in a high-quality chemistry journal. [As always, there are exceptions: η6-benzene coordinated to metals is nearly always drawn with the circle, for example, but that is really a different story altogether.] Furthermore, using the circle makes it infinitely harder to explain a lot of aromatic chemistry: o/m/p-directing effects of substituents, or kinetic/thermodynamic sulfonation of naphthalene, to give two very basic examples.
The alternative to this is to be a purist: we must always draw dashed lines, and everything else is "wrong". If you want to be in that camp, so be it: congratulations, you are technically correct, but at what cost? Even IUPAC, the kings of being technically correct, don't care:
Curves represent delocalization, yet lots of structures have some delocalized elements. Although all such elements could be depicted with curves, there is little gained by doing so. On the contrary, the arbitrary use of curves can draw the viewer’s attention to insignificant portions of a structural diagram, and away from areas that are chemically more important such as an active site or a reactive group. Accordingly, curves should only be used when the delocalization is specifically being highlighted as an important feature of the structure.
When curves are not used, any alternating configuration of double bonds is acceptable within the further constraints discussed in GR-3.5.
Pure Appl. Chem. 2008, 80 (2), 277–410 (emphasis mine).