What a great question! I'd love to hear what others have to say, but here are the guidelines I use.

The high-altitude premise: scope is used as the "glue" that we use to communicate between the parent controller, the directive, and the directive template.

Parent Scope: scope: false, so no new scope at all

I don't use this very often, but as @MarkRajcok said, if the directive doesn't access any scope variables (and obviously doesn't set any!) then this is just fine as far as I am concerned. This is also helpful for child directives that are only used in the context of the parent directive (though there are always exceptions to this) and that don't have a template. Basically anything with a template doesn't belong sharing a scope, because you are inherently exposing that scope for access and manipulation (but I'm sure there are exceptions to this rule).

As an example, I recently created a directive that draws a (static) vector graphic using an SVG library I'm in the process of writing. It $observes two attributes (width and height) and uses those in its calculations, but it neither sets nor reads any scope variables and has no template. This is a good use case for not creating another scope; we don't need one, so why bother?

But in another SVG directive, however, I required a set of data to use and additionally had to store a tiny bit of state. In this case, using the parent scope would be irresponsible (again, generally speaking). So instead...

Child Scope: scope: true

Directives with a child scope are context-aware and are intended to interact with the current scope.

Obviously, a key advantage of this over an isolate scope is that the user is free to use interpolation on any attributes they want; e.g. using class="item-type-{{item.type}}" on a directive with an isolate scope will not work by default, but works fine on one with a child scope because whatever is interpolated can still by default be found in the parent scope. Also, the directive itself can safely evaluate attributes and expressions in the context of its own scope without worrying about pollution in or damage to the parent.

For example, a tooltip is something that just gets added; an isolate scope wouldn't work (by default, see below) because it is expected that we will use other directives or interpolated attributes here. The tooltip is just an enhancement. But the tooltip also needs to set some things on the scope to use with a sub-directive and/or template and obviously to manage its own state, so it would be quite bad indeed to use the parent scope. We are either polluting it or damaging it, and neither is bueno.

I find myself using child scopes more often than isolate or parent scopes.

Isolate scope: scope: {}

This is for reusable components. :-)

But seriously, I think of "reusable components" as "self-contained components". The intent is that they are to be used for a specific purpose, so combining them with other directives or adding other interpolated attributes to the DOM node inherently doesn't make sense.

To be more specific, anything needed for this standalone functionality is provided through specified attributes evaluated in the context of the parent scope; they are either one-way strings ('@'), one-way expressions ('&'), or two-way variable bindings ('=').

On self-contained components, it doesn't make sense to need to apply other directives or attributes on it because it exists by itself. Its style is governed by its own template (if necessary) and can have the appropriate content transcluded (if necessary). It's standalone, so we put it in an isolate scope also to say: "Don't mess with this. I'm giving you a defined API through these few attributes."

A good best practice is to exclude as much template-based stuff from the directive link and controller functions as possible. This provides another "API-like" configuration point: the user of the directive can simply replace the template! The functionality all stayed the same, and its internal API was never touched, but we can mess with styling and DOM implementation as much as we need to. ui/bootstrap is a great example of how to do this well because Peter & Pawel are awesome.

Isolate scopes are also great for use with transclusion. Take tabs; they are not only the whole functionality, but whatever is inside of it can be evaluated freely from within the parent scope while leaving the tabs (and panes) to do whatever they want. The tabs clearly have their own state, which belongs on the scope (to interact with the template), but that state has nothing to do with the context in which it was used - it's entirely internal to what makes a tab directive a tab directive. Further, it doesn't make much sense to use any other directives with the tabs. They're tabs - and we already got that functionality!

Surround it with more functionality or transclude more functionality, but the directive is what it is already.

All that said, I should note that there are ways around some of the limitations (i.e. features) of an isolate scope, as @ProLoser hinted at in his answer. For example, in the child scope section, I mentioned interpolation on non-directive attributes breaking when using an isolate scope (by default). But the user could, for example, simply use class="item-type-{{$parent.item.type}}" and it would once again work. So if there is a compelling reason to use an isolate scope over a child scope but you're worried about some of these limitations, know that you can work around virtually all of them if you need to.

Summary

Directives with no new scope are read-only; they're completely trusted (i.e. internal to the app) and they don't touch jack. Directives with a child scope add functionality, but they are not the only functionality. Lastly, isolate scopes are for directives that are the entire goal; they are standalone, so it's okay (and most "correct") to let them go rogue.

I wanted to get my initial thoughts out, but as I think of more things, I'll update this. But holy crap - this is long for an SO answer...

PS: Totally tangential, but since we're talking about scopes, I prefer to say "prototypical" whereas others prefer "prototypal", which seems to be more accurate but just rolls off the tongue not at all well. :-)

My personal policy and experience:

Isolated: a private sandbox

I want to create a lot of scope methods and variables that are ONLY used by my directive and are never seen or directly accessed by the user. I want to whitelist what scope data is available to me. I can use transclusion to allow the user to jump back in at the parent scope (unaffected). I do NOT want my variables and methods accessible in transcluded children.

Child: a subsection of content

I want to create scope methods and variables that CAN be accessed by the user, but are not relevant to surrounding scopes (siblings and parents) outside the context of my directive. I also would like to let ALL parent scope data to trickle down transparently.

None: simple, read-only directives

I don't really need to mess with scope methods or variables. I'm probably doing something that doesn't have to do with scopes (such as displaying simple jQuery plugins, validation, etc).

Notes

• You should not let ngModel or other things directly impact your decision. You can circumvent odd behavior by doing things like ng-model=$parent.myVal (child) or ngModel: '=' (isolate).
• Isolate + transclude will restore all normal behavior to sibling directives and returns to the parent scope, so don't let that affect your judgement either.
• Don't mess with the scope on none because it's like putting data on scope for the bottom half of the DOM but not the top half which makes 0 sense.
• Pay attention to directive priorities (don't have concrete examples of how this can affect things)
• Inject services or use controllers to communicate across directives with any scope type. You can also do require: '^ngModel' to look in parent elements.

After writing a lot of directives, I've decided to use less isolated scope. Even though it is cool and you encapsulate the data and be sure not to leak data to the parent scope, it severely limits the amount of directives you can use together. So,

If the directive you're going to write is going to behave entirely on its own and you are not going to share it with other directives, go for isolated scope. (like a component you can just plug it in, with not much customization for the end developer) (it gets very trickier when you try to write sub-elements which have directives within)

If the directive you're going to write is going to just make dom manipulations which has needs no internal state of scope, or explicit scope alterations (mostly very simple things); go for no new scope. (such as ngShow, ngMouseHover, ngClick, ngRepeat)

If the directive you're going to write needs to change some elements in parent scope, but also needs to handle some internal state, go for new child scope. (such as ngController)

Be sure to check out the source code for directives: https://github.com/angular/angular.js/tree/master/src/ng/directive
It greatly helps on how to think about them