That depends. Right now, no.
1. If your money just sits in a bank (i.e. does not get loaned out) then it is as if the money didn't exist - it does nothing for the economy. If you spend the money instead, then it does increase the economy. So if the bank isn't making loans (either because it doesn't want to lend or because no one wants to borrow, then saving money in a bank may be good for you but hurts the economy instead of helping it.
This is where we are now:
http://krugman.blogs.nytimes.com/2009/07...
Corporations and banks are sitting on tons of cash (the banks have more than $1 trillion in excess reserves sitting at the Fed) with no good (i.e. profitable) investments in sight.
2. Under normal circumstances, there is an optimal level of investing. Too little and the economy can't keep growing; too much and the investments become useless:
http://belfasttelegraph.co.uk/news/l...
As long as the current level of investment is lower than the optimum and your savings will get lent out to produce more investment, then additional savings help the economy.
On the other hand, even before the recession there was a global savings glut:
http://federalreserve.gov/boarddocs/...
http://en.wikipedia.org/wiki/Global_saving_glut
http://krugman.blogs.nytimes.com/2010/03/16/capital-export-elasticity-pessimism-and-the-renminbi-wonkish/
which meant that there were more savings than the optimum level of investment. One result was that many of the investments made would never be profitable.
Some argue that this was a major factor in the recession and its severity.
3. On the other hand, most of the time, most economies can use more investment than they get.
http://books.google.com/books?id=DjKBjuj2ktEC&pg=PA128&lpg=PA128&dq=domestic+savings+asian&source=bl&ots=BNLq_kwfyz&sig=H1HlAlypekZ5nAtqOm-Z4mMMFyQ&hl=en&ei=ztsjTeOBE5SosQOy16SLCw&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDkQ6AEwBA#v=onepage&q=domestic%20savings%20asian&f=false
It was domestic savings that funded the investment created the "Asian Tigers"
http://en.wikipedia.org/wiki/Four_Asian_Tigers
http://galbithink.org/topics/ea/save.htm
