It is common to look at visibility and cloud clearance at the same time. However, this can often make it harder to remember all of the different rules. Here is the simplified set of rules just for visibility. I find that it is much easier to memorize the 3 rules below than to study the full chart with all of the information.

All visibility restrictions are measured in statute miles.

These rules apply to all airspace except A unless specifically mentioned.

These rules are for fixed wing airplanes. The rules vary for other types of aircraft, like helicopters.

1. In most cases, the required visibility is 3 statute miles.
2. If you are above 10,000 feet above mean sea level (MSL) then you need 5 statute miles of visibility. The air is thinner so the airplanes are moving a lot faster and you need more time to see them. Also, at higher altitude, you are more likely to encounter IFR traffic and you need time to see these planes after they pop out of a cloud.
3. However, during the day only, if you are in class G airspace (flying very low) then you need just 1 statute mile of visibility. Class G airspace often extends up to 700 feet above ground level (AGL) or 1,200 feet AGL. In the image below, see the shaded magenta line. On the soft side of the line (near Smoketown airport), class G extends up to 700 AGL, but on the hard side of the line (near Hideaway airport) class G goes up to 1,200 AGL. Airplanes flying low tend to be flying much slower, so with 1 mile visibility they are expected to have enough time to see and avoid each other.

Rare Exceptions

1. If it is daytime and you are flying along very high terrain that puts you both above 10,000 MSL and below 1,200 AGL then the class G rule applies and the requirement is 1 mile visibility. It’s hard to imagine a situation where flying VFR at a high altitude, probably near mountains, and with just one mile of visibility would really make sense, but that is the rule.
2. There are some remote places where class G airspace extends up to 14,500 MSL, like in Alaska. For example, see the blue shaded line in the image below. On the soft side of the line (near Sparrevohn airport), class E airspace begins at 1,200 AGL. However, on the hard side of the line (near Lime Village airport), class G extends all the way up to 14,5000 MSL where class E begins. In these areas, the 1 mile requirement for class G applies until you reach 10,000 feet MSL. When you are above 10,000 but still in class G the 5 statute mile limit (from rule 2 above) kicks in.
3. If you are flying at night in an airport traffic pattern (in class G airspace) within one half mile of the runway, you may fly with just 1 mile visibility. 91.155(b)(2)

Safety

Just because a flight can be completed legally doesn’t mean it is safe. Consider your personal minimums for visibility and decide in each situation if flying in lower visibility is appropriate.

Think of it like this, lower than normal visibility is one part of the accident chain. You can fly like this most of the time, but if you combine it with other factors you could easily build a big enough chain that really does lead to an accident. Is there other adverse weather to contend with? Do you have enough fuel to complete the flight with plenty of reserve? Are you getting distracted from the task of scanning for other traffic?

Make sure to read FAR 91.155 in full after checking out the rules above.