The previous two answers cover the main important points, but there are a few things that should still be mentioned.
First, I should say that I disagree with the extreme minimalist approach to graphing -- that all redundant ink must go. Distracting, non-meaningful variation should go. But a solid area versus a single line can catch the eye better and communicate more at a glance. And as you say, it can add "visual variety".
However, as @xan points out, that quick glance also interprets an area differently than a line, in ways partially subconscious.
An area graph implies a total quantity accumulating as you proceed along the x-axis. If you compare two graphs, and one has a larger area filled in, your glance will tell you that it has a greater total regardless of the start and end values.
In contrast, a line graph shows a changing value. The focus is on the change in position from one point to the next, not on the total accumulated.
So when should you use an area graph?
- when the values represent a clear quantity with a definite zero point shown on the graph;
- when the value represents an amount added (or removed) at each point, such as normal daily rainfall or monthly profit/loss;
- when the value represents a distribution of a population, meaning that the total area under the curve represents the total size of the sample, such as bell curve of the number of students with different grades (basically a smoothed histogram).
The idea is that, when reading the graph, if you take two points on the x-axis, the area shown between them should represent an actual amount of something accumulating in that range. For this reason, if you values include negative amounts I'd recommend using opposite colours for negative and positive areas to emphasize that they cancel out in the total.
When should you not use an area graph?
- when the zero point is arbitrary (as in non-absolute temperature, as @timcdlucas said), invalid (as in measurements that are a ratio of two values, like an exchange rate), or not shown on the graph for space reasons;
- when the values shown by the height of the line already represent a cumulative measure, such as total rainfall to date (for the month/year) or debt/savings;
- when the values represent the position/value of a single changing entity rather than an accumulation;
- when you want to compare multiple lines on the same chart (if you can't see the whole area, you lose the meaning -- compare area charts side-by-side instead).
With those guidelines in mind, your ping graph can be interpreted two ways.
On the one hand, if you think of the ping speed as a as a single variable that changes over the course of the day, then a simple line chart would be most appropriate.
On the other hand, if you were comparing two different networks' daily ping-speed patterns (or the same network on different days / time periods), then maybe you want to emphasize the total amount of time required for network tasks. For example, if your graph had multiple peaks, instead of just one, a line graph would emphasize the variability in speed while an area graph would emphasize total delay.
The cumulative total is slightly greater in the first half of the graph (left of the red line) than the second, even if the peaks hit higher max values on the right. Filling in emphasizes that solid block on the left, so that it balances better against the peaks.
(Forgive the poor image quality -- couldn't figure out how to get R to do an area graph! Had to export and edit separately.)