What do I do against the infamous "gank squad"?

In League of Legends, a "gank squad" can loosely be defined as:

a team of highly coordinate players who focus on demoralizing and map control as opposed to traditional tower pushing and lane control.

These are usually teams of 3 with bursty and/or stun-loaded champions (such as Singed, Vayne, Poppy etc), who sneak around picking off loan champions trying to jungle or hold a tower. This naturally causes a change in behavior for the opposing team to be more paranoid and lose ground as a result (usually due to their ally's doing the dirty work and failing pushes). This tactic has proven highly effective and difficult to coordinate against.

What strategies are effective to counter these "gank squads" to prevent them from demoralizing a team and preventing effective jungling?

Gank squads have three primary advantages: High-burst damage, coordination, and numbers. They rely on the fact that they're better prepared than their victims, at least at the outset of the engagement.

If you can catch them attempting this early, an aggressive warding policy and a decision to shut them down can go a long way. However, this level of coordination is hard to pull off in a non-premade game. Individually in your lane, however, something similar can be accomplished: Aggressively ward the entrances to your jungle, where they're likely to come from and play conservatively. Since they aren't farming, they must get kills in order to scale. If you are premade, and you notice multiple members often missing from lane, aggressively ward jungle entrances and try to catch that squad unprepared.

Obviously, the other problem is their burst. Because burst damage is typically magic damage (at least, until the game gets out of control), a Hex Drinker can go a long way. Any magic resist, however, is a big plus. Since they have to be aggressive, having sufficient magic resist can bait them into overextending into a tower dive. Assuming you have an equal number of teammates, that plus the tower damage can turn the fight in your favor.

Even if you die, your team should try to use the fact that they saw 3 enemies in your lane and try to make the most of it, be it being aggressive in lane knowing the jungler can't gank right now, taking a dragon/their blue or pushing down a tower. So if your are absolutely positive you are going to die, try to spend as much of their time as possible, giving your team more time to do something else elsewhere.

The ultimate point being that after a few failed attempts, the gank squad won't be strong enough to be as big of a threat.