A run-on sentence is a sentence that either goes on longer than it should or is missing a crucial piece of connecting tissue between two independent clauses.
Comma splices
A run-on sentence with a comma splice consists of two independent clauses separated by a comma and missing a conjunction—for example:
I need a new TV, mine’s broken.
The movie was good, the special effects were awesome.
These could be corrected in a number of ways. The two clauses could be made separate sentences:
I need a new TV. Mine’s broken.
The writer could replace the comma with a semicolon:
The movie was good; the special effects were awesome.
An em-dash can do the same thing:
I need a new TV—mine’s broken.
With a subordinating conjunction, one clause could become dependent on the other:
Because the special effects were awesome, the movie was good.
Or the writer could link them with a coordinating conjunction:
My TV’s broken, so I need a new one.
Two sentences crammed together
Other run-on sentences consist of two independent clauses crammed together with no punctuation—for example:
Let’s go it’s getting hot.
All of the comma splice solutions apply here as well:
Let’s go. It’s getting hot.
Let’s go; it’s getting hot.
Let’s go—it’s getting hot.
Since it’s getting hot, let’s go.
It’s getting hot, so let’s go.
Conjunction misuse
Another common type of run-on sentence involves misuse of conjunctions, especially however, often with a comma splice—for example:
I have kits to assemble, however, I have no bags.
Here, there’s a comma splice after I have kits to assemble. This common error probably results from confusion with perfectly acceptable constructions like this:
Over many years of jurisprudence, however, the Supreme Court has ruled that most of the rights protected in the Bill of Rights also apply to the states. [SCOTUS Blog]