How can Erlang C values be greater than one? Here is an Erlang C plot I did myself. The x-axis represents the total traffic while the y-axis represents the probability. Each line represents a different number of total available channels.

As you can see, the graph has probabilities greater than one. How can this be even possible?

The formula is only valid under the assumption $A<c$.
In the formula, $A$ measures the average intensity (e.g., in the rather dated call-center application, the average number of calls you have at any given moment), while $c$ measures the number of channels (in the same model, it's the number of calls you can process at any given moment).
When $A<c$, the system will be ergodic: sometimes you will have calls (or whatever) pile up, but on average, they will be processed faster than they appear, and long-term behavior is stable. We can compute properties of the typical state of the system; in particular, the probability that all channels are busy.
When $A\ge c$, the expected long-term behavior of the system is divergent: calls keep piling up faster than they can be handled, so that the number of waiting calls is proportional to the time. This is not surprising: if $A = 20$ and $c=10$, then this says that you're getting an average of $20$ call-hours per hour, but can only process at most $10$ call-hours per hour, so you get $10$ extra call-hours per hour that went unhandled.
In this case, there is no "typical state" and the usual analysis we can do is nonsense. We should ignore the formula, which gives a probability greater than $1$ for $A>c$, and just say "our analysis of the system says that everything goes horribly wrong in this case". 
