If I had this amount of money, I personally would probably try to pay off as much of my mortgage as possible. This would greatly help me financially as it would lower the amount of money I pay on a mothly basis. I could invest it, but to be honest, as I am somebody who hates being in debt, I would prefer to get rid of as much debt as possible.
What would be done with the $100,000 is dependent to a large extent on your present financial state and age. If I were living in a small house with just the basic necessities or were very old, the best idea would be to spend the money. I would get myself all that I wanted and which can be bought with the $100,000. It would make little sense for me to invest the money and continue to live in the same financial state or invest it when I would no longer be around to enjoy the benefits of the the investment growing larger.
Paying off any high interest debt I had would be my first order of business, as since credit cards and the like often charge 15% - 18% interest, that is a considerably higher return than most investments can bring you. It also raises your credit rating which might save you thousands in the long run with other loans you may seek.
Secondly, I would invest it so that I have either a nest egg for retirement or some additional income in the near term.
With $100,000 I would pay off any debts I had and invest in an established retail business with half the money and use the retail business as a source of income.
I'd put left over money in a CD and make a definite plan as to how long I would leave it there to amass interest and grow. Maybe I'd make a ten year plan and look to combine and interest from the CD with money made (and saved) from business profits and invest in another business and begin the cycle again.
After paying off debts, and some debts of my progeny, I would establish a scholarship at the high school where I taught. And, of course, buy some gold. (One's age does determine the directions of money)
Since I'm retired, I would also invest it but not in the long-term investments mentioned by previous posters. At my stage of life, I would be rather conservative with most of it - I don't have a whole lifetime to recuperate from a major decline in the value of my portfolio.
I would invest it. However, the real question is where you would invest. I would try to diversify a little. I would put 25% of the money is precious metals. I would try to put a down payment on a rental property, as long as I could make the monthly payments. After this, I would put the rest in a company that is under-valued.
I would invest it in a fairly diverse array of places. Perhaps some mutual funds, some in CDs or T-notes, and maybe a bit of it in higher risk investments. Depending on the market, I might even gamble some of it on real estate. And depending on the person, it's also wise to use it to pay off unsecured debt and auto loans.
If you look at it from an economic perspective, what you should do with the money is invest it. That way you will end up with more money in the end. Investment is how economic growth happens for countries and it can be seen in the same way on the personal level.
Don't forget to donate to a cause, not only is there an economic value with that action but an immense boost to your utility as a person :)
If I had the money, I will do a short-term investments, such as: stocks, bonds...