Do molecules with a hexagonal planar geometry exist? I recently read an article on Wikipedia about pentagonal planar geometry.

There are only two molecules with this kind of geometry $\ce{XeF5-}$ and  $\ce{IF5^2-}$  and it has two electron pairs at the axial positions. 

As soon as I looked at this, I thought that hexagonal molecular geometry can also exist much the same way i.e. 6 substituents bonded to the central atom and two lone pairs at the axial positions opposite to each other.

On the page, its given that arrangement of 6 atoms in a plane is found in higher coordination states but that does not help either as they have not given any examples of that.

Do hexagonal planar molecules exist, and if they do, what are they?
I think it's nearly impossible to find or synthesize a "canonical" complex with hexagonal molecular geometry, but in the field of host-guest supramolecular chemistry there are numerous examples of "unusual" geometry. Probably the most well-established class of such compounds are torands ("hosts") incorporating alkali metal cations ("guests").

Check out, for example: (1) Bell, T. W.; Cragg, P. J.; Drew, M. G. B.; Firestone, A.; Kwok, D.-I. A. Angew. Chem. Int. Ed. Engl. 1992, 31 (3), 345–347, DOI 10.1002/anie.199203451.

Here is an example of the structure with potassium ion from (1), Tri-n-butyltorand-potassium picrate clathrate, which I quickly sketched in Olex2:

Top view:


Side view:


Unit cell and packing: