I've never been sure if it's entirely true, but I recall being told 30 years ago when I was first starting out as a "Chartist" - that's what Technical Analysts used to be called! - that many people used a 200 day moving average because that was the maximum number of periods that chart machines could calculate! The funny thing is, even today the 200 day moving average is quite commonly quoted by market commentators.  I've no idea why, but people must have their reasons, surely?  

During these past 30 years, I have come across countless moving average combinations.  In the early days, technology was a limiting factor, many people at that time used a single moving applied to a daily chart.  I recall 30 or 50 days quite commonly being used for a Short-term trend with 100 or 200 days for the long-term trend. Some people would then try to be clever and use slightly shorter numbers than these, perhaps 25 & 90 days in order to "get an earlier signal" than the market at large.

I myself have experimented with all sorts of moving average combinations and have long since come to the conclusion that the best combinations are the ones which make the most "logical sense" from a market timing aspect.  EG a day, a week, a month, quarter, a year.  I actually look at all sorts of time-frames from intra-day to multi-year and below I give some examples of the combinations I use.

Intra-day charts (15 minute bar) 16, 32 & 96 period (4, 8 & 24 hour) combination.
Week+ view (1 hour bars) 24, 60 & 120 hour combination.
Month+ view (4 hour bars) 30, 60 & 132 period (5, 10 & 22 day) combination.
6-12 month view (daily candles) 22 (1 month), 65 (3 month) & 260 (12 month) combination.
Multi-year view (weekly candles) 13 (3 month), 52 (12 month) & 260 (5 year) week combination.

Here are two recent examples of the 260 day moving average being a better trend indicator than 200 days. In the case of USD/JPY (left chart) the 200 day line took people out of longs in May & July, whereas the 260 day correctly kept bulls in.  In the case of USD/CHF, the 260 day line correctly triggered signaled a major trend reversal in July, whereas the 200 day line would have resulted in a month of whipsawing.  



Left chart - USD/JPY daily chart.  Right chart USD/CHF daily chart. (Click on the chart to enlarge)

Please note, I would never advocate use moving averages in isolation and personally I always use them in combination with an MACD indicator, also looking for the likes of trend lines & channels, Fibonacci retracements & projections.  Also, be sure to never overlook the basics, such as chart patterns and recent price history to avoid falling into a trap!