If you are Indian, then ICICIDirect provides International trading in a few scrips via their trading account. It probably won't be a good idea though to open such an account just for buying and keeping a few shares as the account will have additional charges like annual maintenance and other expenses which will reduce whatever profits you may or may not make. These are advisable if you trade regularly. Check the additional expenses and then calculate.
Other Brokerages might also provide such services.
Instead of multigiant Blue-chip is the word used in the industry for such companies. You can also look at Indian companies to invest as there are very good companies in every market.
last 2 years comparison between microsoft, ibm, tcs, infosys and google. I am almost sure this does not include dividends.
http://in.finance.yahoo.com/q/bc?s=MSFT&c=IBM,TCS.NS,INFY.NS,GOOG&t=2y
TCS has outperformed all of these but there will also be many others which will have a better record than TCS. This is just an example of options available locally and in the IT sector. I have not even looked at other industry sectors.