Q:

What area does the Hallow spell actually cover?

When discussing ways to take down Count Strahd von Zarovich in my CoS campaign, my players considered casting the Hallow spell and covering literally all of Barovia in hallowed ground. They figured they can do this because of the text of the spell (PHB Page 249): 

Hallow
You touch a point and infuse an area around it with holy (or unholy) power. The area can have a radius up to 60 feet, and the spell fails if the radius includes an area already under the effect of the hallow spell.
(Emphasis Mine, 6th Printing of PHB)

So because of how the spell is written, there is no shape defined. Maybe sphere is implied by the use of a radius, but they also figured they could simply opt for a smaller cube shape that would fit within that sphere, because it is not explicitly defined. With that in mind, they will not have any overlapping because you can fit cubes together perfectly. Looking at the Areas of Effect on pages 204 and 205 we can see that Sphere says this:

Sphere
You select a sphere's point of origin, and the sphere extends outward from that point. The sphere's size is expressed as a radius in feet that extends from the point. 

As far as I (and one of my players helping me research this) have found, every spell that expresses that it is a sphere whether or not it gives you a specific radius or says "up to [some] radius." It could simply be a circle, but there needs to be a three-dimensional area that it affects, so that is the same as making it a limitless cylinder.
So is it actually a Sphere or is it just some shape that fits within the boundaries?

A:

I would allow players to make the spell cover any shape they wanted, provided that shape is simply defined, contiguous, has no "islands" or "doughnut holes", and no part of it is further than 60ft from the point they touch while casting the spell. By "simply defined", I mean simple shapes (cube, sphere, etc), or anything that can be expressed simply and obviously, like "inside the house" or "the area under the bridge".
I came to this ruling because it leaves maximum scope for the players to do what they want, while minimising the number of ways that it can become complicated, boring or overpowered.
Analysing the rules
Generally, where things are vague in 5e, the best way to approach it is thus:

Do other rules have anything related to say?
How would players generally be expected to use it?
Which interpretation causes fewer complications?
Which interpretation protects against abuses or ways to bypass balancing mechanisms (action economy, spell slots, etc)?

Related rules
The section on spellcasting doesn't mention how to handle spells that don't use one of the listed shapes. However, the alarm spell can be cast to cover "an area within range that is no larger than a 20-foot cube", which means there is precedent for choosing your own shape of area, within certain size constraints.
Expected use
I'd expect players to use hallow to protect areas like the inside of a place they're staying in - a house, a castle, a cave, whatever. This could be any shape, really, and as a DM there's no reason to want to spoil that for them.
Complications
Circles don't tessellate, and the players may wish to cover larger areas. Handling the bits of a circle that protrude out through the walls of a square house may be tricky (if you rule that this happens).
Balancing
The 24-hour casting time and 1000GP cost protect against serious abuses, and with those in place, I can't see a particular way that one shape is "overpowered" compared to another.
Ruling
Given these observations, I see no problem in letting players choose any shape they like. Of course, the spell says "you touch a point, and infuse an area around it", so no part of that shape can be more than 60ft from the point they're touching. This means that to cover a corridor that's 120ft long, you'd have to cast the spell from the middle. For the sake of keeping things simple, I'd probably also say that the area can't have "islands" in it - for example, you couldn't hallow a doughnut shape; you'd have to cover the bit in the middle. (This also prevents you from using hallow to trap things in the middle, which is the only thing I can see that might be open to abuse.) Likewise, you can't use one casting of hallow to cover two separate but unconnected areas, even if both of them fall within the spell's range. The hallowed area must be contiguous.
Reasoning
Letting the player pick the shape covers their intended uses, while also preventing situations that are either fiddly to manage or detrimental to the game's balance. In other words, it streamlines the playing of the game without blocking anything that's fun or adding anything that makes it less fun - which is the mark of a good rule.
For some examples, consider the following scenarios:

The players want to hallow the inside of a small house, without having gaps at the corners or weird curved segments of hallowed ground outside it. Letting them choose the shape lets you divide it simply into "inside = hallowed" and "outside = not hallowed".
The players want to hallow a larger area. Letting them pick the shape lets them choose a shape that tessellates. If you're playing on a square grid, they can hallow cubes; if you play on a hexagonal grid, they can hallow hexes. If they want, they can pick other shapes that fit the terrain, like "up to the edge of the cliff" or "120ft of road".
The players want to hallow a small building, but the building is shaped such that they can't see all of it at once (perhaps three sides of a square). Letting them pick the shape lets them hallow it all in one casting provided that it's small enough. Given two buildings of equal floor area where one can be hallowed in one casting but the other takes several because of its shape is needlessly complicated for little gain in entertainment value.

A:

Regardless of the shape of the hallow spell's affected area, I think your players need a new plan. There are some rather hefty constraints on their ability to cover all of Barovia in hallowed ground.

Casting Hallow consumes 1000gp worth of material components.
Hallow has a 24 hour casting time.
Hallow covers at most π·60² ≈ 11310 ft²

Consider the smallest country in the world - Vatican City, which has an area of 0.44 km² (4736121 ft²). Assuming perfect packing, it would require roughly 4736121 / 11310 = 419 castings of Hallow to cover the entire country. That's 419,000 gold of materials, and 419 days for Strahd to figure out what they're up to. And that's just for a country the size of Vatican City, which is tiny - you can walk across it in under an hour. If Barovia is closer in size to Germany, for example, you're looking at 340,000,000 castings of Hallow for complete coverage. I rather suspect your players will be long dead before they complete the 930,000 years worth of spellcasting to pull that off.

A:

Rules as written: Sphere or cylinder
The key phrase in the text concerning the area is

The area can have a radius up to 60 feet

The way it's phrased implies the area always has a radius and you only get to choose the size. Spheres and cylinders are the only two shapes in the rules expressed in terms of a radius (Player's Handbook p.204). Besides that, the rules rely on common English so we can safely exclude rarer definitions of radius (e.g. the radius of a regular polygon.)
Note that other spells which let you freely choose an area say it must be contained within some shape rather than talking about the area's dimensions:

Alarm: "Choose a door, a window, or an area within range that is no larger than a 20-foot cube."

Move Earth: "Choose an area of terrain no larger than 40 feet on a side within range."

Antipathy: "You target something within range, either a Huge or smaller object or creature or an area that is no larger than a 200-foot cube."

Rules as intended: Probably not a sphere
The simplest way to say the shape is a sphere is to refer to it as such. Plenty of other spells do this already (e.g. Antimagic Field, Wall of Ice, Tiny Hut, Resilient Sphere.) If the area is intended to be a sphere, the writers chose a convoluted way of saying so.
I suspect the shape is meant to be a cylinder of infinite height. Using the term cylinder could've been seen as confusing since the spellcasting rules specify cylinders have a fixed height.
A cylinder shape is also consistent with the popular trope that fiends and undead can't enter hallowed ground at all.
Rules as fun: Making this work

Accept the gaps.
If the cylinders are packed tightly, creatures that can't enter the areas can't reach (or leave) the gaps except through teleportation.

Relax the no-overlap rule
The main purpose of the no-overlap restriction is probably to prevent you from stacking multiple effects. You can easily allow hallowed areas to overlap if they're identical. This is equivalent to allowing them to tessellate with regular hexagons, plus some extra area at the edges.

