Having over a dozen apps out on the market, we noticed that every time we release an update, we have a spike in downloads. The reason is that, when publishing an update, the app market gives you a bust of ranking so you get more often in the search results and may be listed on the first page of rating within the category in which your app belongs to. In addition, surprising users with improvements (hopefully), either its some new features or a holiday re-skining of the UI, works as a gentle reminder and can increase the number of active users which is very important..
Another observation, more obvious this time, is that people tend to download and explore new apps on weekends.
Here is an example of the downloads statistics on ChildrenTV, on the right side you see the number of downloads on the left I showed the weekend days.
Another advise would be - Know your users.
Try to analyze and put yourself in your user's shoes. Imagine his life cycle and try to understand at what point you (your app) can be useful. When is your user more willing to use your product.
Here is an example from the same app, Children TV. Take a guess which is the reason of a massive increase in downloads on this statistics.
If you pay attention to the dates you will see that on vacation the downloads are considerably higher, parents are happy to get their kids busy, kids are happy to watch their favorite cartoons. Boom, mission accomplished.
I will keep updating this article as I notice new external factors influencing downloads, full moon for example :).
