grammar

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: http://grammar.quickanddirtytips.com/run-on-sentences.aspx - 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:

DEATH SENTENCE
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