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超{こ}える, 越{こ}える and 過{す}ぎる are said to mean " _to pass through_ " in the
"edict" dictionary, but I don't fully understand the difference between the
three.

How does their usage differ please? Can anyone provide any relevant examples?

One example that I'd like to express, but don't quite know how to, is how to
say " _to pass a peak of a mountain_ " or " _to pass a peak point on a graph_
", but I'm not even sure these are the right words to do that.
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usage verbs word-choice
The difference between 超{こ}える,  越{こ}える and 過{す}ぎる
`過{す}ぎる` implies the process of passing though. `越{こ}える` and `超{こ}える` mean
'exceed'. In this example:

> × 20kgを過{す}ぎる荷物{にもつ}は機内{きない}に持{も}ち込{こ}めません。  
>  20kgを超{こ}える荷物{にもつ}は機内{きない}に持{も}ち込{こ}めません。

the weight of a luggage is a static property, and a luggage does not grow, so
`過{す}ぎる` cannot be used. In this example:

> 目的{もくてき}地{ち}を過{す}ぎてしまった。  
>  △ 目的{もくてき}地{ち}を超{こ}えてしまった。

`過{す}ぎる` is more appropriate than `超{こ}える` because there is no inherent notion
of excess among locations (unless a context is set such as to provide the
origin of measurement). Rather, the process of passing through is the
intention of this expression.
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Another difference is that 過{す}ぎる is one of the super-useful suffixes, as you
can attach it to any verb or adjective. As a suffix I believe it generally
takes on the sense of excessivity, but I think there may be other senses for
it as well.

For **verbs** you use the 連用形{れんようけい} (i-form):

> 五段{ごだん}：飲{の}む → 飲{の}みすぎる  
>  一段{いちだん}：食{た}べる → 食{た}べ過{す}ぎる  
>  サ変{へん}：勉強{べんきょう}する → 勉強{べんきょう}しすぎる

It attaches directly to **na-adjectives** :

> 変{へん} → 変{へん}すぎる

But you have to drop the い for **i-adjectives** :

> 怖{こわ}い → 怖{こわ}すぎる
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sawa gave an excellent post already, but there are a couple of cases where
I've found exceptions. I'd also like to elaborate on the differences between
`超{こ}える` and `越{こ}える` a bit using the Microsoft IME as a reference.

One exception to sawa's post is passing mountains or obstacles seems to use
`越{こ}える` instead of `過{す}ぎる`. sawa also commented that when `過{す}ぎる` is added
to verbs and adjectives (e.g. `高{たか}すぎる`) that it means "exceed" instead of
"pass" like it would by itself. However, it should be noted that
`通{とお}り過{す}ぎる` means "to pass" or "pass through". As istrasci has noted in the
comments though, this is not an exception but a separate verb in it's own
right.

**`越{こ}える` is used for:**

  * Passing a mountain: `山{やま}を越{こ}える`
  * Passing obstacles: `障害{しょうがい}を越{こ}える`
  * Exceeding a point: `点{てん}を越{こ}える`
  * Exceeding time: `時{とき}を越{こ}える`

**`超{こ}える` is used for:**

  * Exceeding an amount: `数量{すうりょう}を超{こ}える`
  * Exceeding a standard or reference: `基準{きじゅん}を超{こ}える`
  * Exceeding a limit: `限度{げんど}を超{こ}える`

  
Also, here's some some other words similar to those listed using
[Daijirin](http://en.wikipedia.org/wiki/Daijirin) as a reference:

  * Passing a place: `場所{ばしょ}を通{とお}る`
  * Passing days or months: `経{た}つ` and `去{さ}る`
  * Passing months or years: `経過{けいか}する`
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