For a long term investor seeking Growth or regular income there are a few options.
1. Mutual Funds in India:
You can open a NRI/NRO account in India(any bank can do this) and if you have a PAN card, you can invest in mutual funds.
For this, you can directly contact the mutual fund company and send the application. Other option is doing thru online website. I recommend FundsIndia.com as their process is simplified and i am happy with the service. Please note you have to send KYC application first time.
Pl note funds can be repatriated if you do all transactios thru an NRE account.
For equity based schemes there is no tax if you hold the fund for more than 3 years
For debt based funds there is tax(if you hold more than 3 yrs, you get indexation benefit)
2. US based ETFs/Funds:
If you are US NRI, you can invest in ETFs that trade in US market or mutual funds(Mathews has the best India fund)