Why do they do this? Airlines make these changes for a number of reasons, including switching aircraft (which may equate to faster flight times or different seat configurations), or removing a flight from the schedule. The majority of cases I have seen had very minor changes (for example flights leaving 5 minutes earlier or arriving 10 minutes later) with little to no effect on travel.
If there is a change you will be notified by the airline (or your travel advisor, depending on how the ticket was purchased). Airlines will usually contact you direct when changes are within 2-3 days of departure. For this reason it is important airlines have your contact information (in fact, it is now required).
Most often, schedule changes have little impact on travel. An exception, however, is when connecting flights are involved.
Always try to book all flight segments on one ticket, either the same airline or within the same alliance. When segments are all on one ticket, airlines are obligated to put you on the next available flight all the way through to your final destination. If you have separate tickets, airlines have no obligation to make sure the new flights coincide with any connections you need to make.
Avoid the last connection of the day.
It is not always possible to book segments together on one ticket. If you are connecting to a flight booked on a separate ticket, give yourself plenty of time between arrival and departure. When booking on one ticket, airlines automatically calculate their legal connection times. Each airline has their own standards, depending on the hub it serves. Domestically (within the US) I have seen times as low as 30 minutes. Typically it is around 60-90 minutes domestically, and 2+ hours for international connections, though I had clients this month with just over 60 minutes to connect to their international flight. Doable, but not recommended.
Save time deplaning by sitting near the front of the aircraft when connections are tight.
Be realistic. Most of us don't like sitting around airports and thus try to minimize connection times. But tight connections simply increase stress levels and increase the potential for issues to arise. If there are mobility issues, this too needs to be figured in to the time. It takes time to get off the aircraft. And invariably it never fails that the arrival and departure gates are never close together.