Though this 'guide' was inspired by Apocalypse, it's true that in any X-COM game, you'll want your soldiers to be taking cover to reduce the likelihood of injury and death. As a commander, being able to identify good cover locations for your soldiers and taking advantage of that cover is vital to survival and success.
Cover can be fundamentally divided into two categories, along with two "sort-of" categories;
This is anything that absorbs at least one projectile hit of any kind and offers partial protection to standing or crouching soldiers. Common forms of soft cover include low walls, fences, bushes and plants, tables and chairs, bus stops, telephone poles, and so on and so forth. Sheet glass and windows don't really count since they're simply see-through walls and tend to break in a single hit, but they work in a pinch.
Soft cover like thin walls can sometimes offer protection from explosions, but don't count on it.
It should be noted that, if alien weapons of any kind are involved, most items that can be seen as Hard Cover are suddenly classified as Soft Cover. Keep this in mind when fighting aliens, or hostiles using alien weaponry.
This only offers line-of-sight protection - that is, it prevents enemies from seeing you - and no real protection of any kind against actual attack. To put it simply; smoke grenades and explosions make lingering visual cover.
Smoke can be vital for covering an approach or breaking an enemy's line of sight long enough to find better cover if your troops would otherwise be pinned down.
This is anything that absorbs multiple basic small arms hits like large columns, thick walls, UFO hulls and so on. They often impede explosive shockwaves. Alien ship hulls could be considered 'ultra hard' cover as they often absorb pretty much all infantry-portable weaponry.
As far as alien weapons are concerned, some items are still hard cover of a sort; buildings, columns and some battlefield objects are composed of multiple pieces that individually act as soft cover, so the structure as a whole can absorb two or three hits.
Better than nothing!
The absolute worst kind of item to hide behind: one that explodes when destroyed. If you find your agents are in explosive cover, move them ASAP. These tend to be 'soft cover' as far as many weapons are concerned.
On the plus side, they can be used as improvised explosives against enemies that are near them.
Whenever you take cover, be aware of the objects on the ground around your agents. If stray shot or explosion hits a dropped weapon it can trigger a chain reaction of additional explosions from other dropped objects that can reach around cover and inflict serious damage. This is particularly common on Alien ships, as the interiors are often cramped and Anthropods and Skeletoids will litter the ground with explosives when they die.