Run-on sentences and those that just run on, and on, and on

Grammar girl has a highly readable explanation of what a run-on sentence is and how to fix one depending on the writing style you want to achieve: - also available as a podcast.

Here is a fun example of a really long sentence, though not a run-on since it is all connected phrases:

Have you heard how Cuthbert Hatch
To find a gas leak struck a match
And thereby hastened his dispatch
To realms unknown to you and me
Who have not yet been foolishly
Inclined to leave posterity
To puzzle for itself just why
We chose to make our fragments fly
Forever upwards to the sky
As Cuthbert did when in the dark
He smelled a smell and sparked a spark
Which sent him rising like a lark
--A very shattered fowl it's true
With no bit large enough to stew,
And nothing any cat could chew--
Into the unresisting space
Where there is never any place
To rest one's feet or wash one's face
Though this for faceless, feetless folk
As Cuthbert was my then, poor bloke,
Is not by any means a yoke
Which is impossible to bear
For it's with truth that I declare
That cases are extremely rare
Of people ceasing to exist
And then, assuming they'll be missed,
Proceeding forthwith to insist
On spreading sadness with their pen
Among their former fellowmen
With news of things beyond their ken
By writing letters to the press
To say that they are in a mess
Which words in print cannot express
For they're aware that we below
Quite rarely care just how they go
And once they're gone don't want to know
The finer details of the fate
Which suddenly transformed their state,
From Man Alive into The Late
Lamented such as Cuthbert Hatch
Who found that leak with lighted match
And who thereafter failed to catch
The interest of the public eye
Or stir mankind to spare a sigh
--which may explain precisely why
I think that Cuthbert Hatch (the Late)
Would not expect to read (or rate)
A second sentence on his fate?
-John Slim