If you are in Asia, you can buy or sell bitcoin or store it safely in any of the online wallets provided for free by these companies:
CoinHako (Supports China, Japan, and most parts of Asia. It’s based in Singapore, and has excellent customer support both online and via phone): https://www.coinhako.com/users/sign_up
OkCoin (One of the leading bitcoin buying and selling exchanges for both Chinese residents and citizens throughout Asia): https://www.okcoin.com/
Huobi is exclusively for China but may serve other parts of Asia as well: https://www.huobi.com/
BTC China. As their company name says directly, they buy and sell BTC for China, may serve most Asian countries, and have secure bitcoin wallets available for their users here: https://pay.btcc.com/
Quoine is an exchange that offers free wallets, mostly for trading with Bitcoin on their exchange. They do let their user’s trade bitcoin in Japanese Yen as well as US Dollars and serve Asia including all of Indonesia. Please be aware that they do NOT support US customers at this time. So be sure to use this one only if you are in Asia, or more specifically, in China, Japan, or surrounding areas. They are a good and stable exchange and have secure wallets, but they can only serve clientele in Asia at this time with them: https://www.quoine.com/
If you’re looking to buy bitcoin or have a wallet specifically in Taiwan, then you may want to use BitoEX which can be found here:
https://www.bitoex.com/users/sign_up
Or, you may like MaiCoin, which is also in Taiwan and boasts the support of having over 130 financial institutions backing them with access to 30,000 ATMs for use to use with their service! https://www.maicoin.com/en/sign_up
If in Hong Kong, you’ll find these two to be good choices for you:
ANXBTC: https://anxbtc.com/
BitFinEx: https://www.bitfinex.com/
For the people of Japan, I would highly recommend Kraken as one of the very best for you: http://www.kraken.com
(Note: Kraken is MASSIVE! They are based in the US, but they serve Canada, Japan, Germany, Italy, Romania, most of Europe and the Americas, too! If in doubt, check them out!)
Although Quoine serves Indonesia completely, one of the best choices to buy and sell bitcoin there and have a free online wallet is Bitcoin.co.id: https://www.bitcoin.co.id/
For our friends in the Philippines, one of the easiest ways to buy bitcoin (and to pay bills or reload your phone) is a site called Coins.ph which you can visit with this link: https://coins.ph/
If you’re in the Philippines and just want to buy bitcoin a little faster, you may also like https://buybitcoin.ph
For the people of Malaysia, you will find these two services to be efficient and just what you need to store bitcoin and also to buy and sell it:
BITX: https://bitx.co/in/global/en/
BTC.my: http://btc.my/
In South Korea, you can use Korbit to buy and sell bitcoin, or have a personal wallet: https://www.korbit.co.kr/
Another good place to buy and sell bitcoin and get a wallet from is Coinplug if you live in Korea: https://www.coinplug.com
As for the good people of India, you have quite a few more choices here:
UnoCoin is one of the most popular choices in your country for Bitcoin, and they have free wallets for everyone who needs one: https://www.unocoin.com/
BTC X India is another popular place to buy and sell bitcoin for you and have a bitcoin wallet online. It is both an exchange and a buying/selling spot for all people in India: https://btcxindia.com
If you prefer to use a service that is mostly mobile-based in India, then you will like the newer Zebpay service (available for both Android and iPhone) which replaced BuysellBitCo.in here: https://www.zebpay.com/
(ZebPay still lets you buy and sell bitcoin and works just as the old site did, but it is under new ownership, new name, and mobile-focused now. I would recommend the other two above if you are looking at having something that works well universally, but if you will be using a mobile phone more than not, then ZebPay would be a good service if you are using your phone mostly)