Coinbase has a "hot wallet" where 1-2% of coins are made available. 98-99% of bitcoins at anytime are stored in a "cold wallet" (offline) at locations across the world. To be truly safe, you can create your own "paper wallet" offline where no one else has access. Think of it as a dollar bill or paper currency. The Winklevoss twins store their BTC on computers in secure locations that never connect with the internet. You could create a brain wallet where you remember the keys. A lot of people just download the bitcoin-qt and store them on their computer. Make sure you encrypt your account if you do this! You can do all this stuff for LTC and most other altcoins. Note: some of the altcoins have sketchy qt wallets and are all-around sketchy.
Thanks for the Info. All coin exchanges need to do that "cold wallet" stuff i mean the hackers are like pirates aboard the exchanges and take all.
I would also say avoid BTC-E especially MT4/BTC-E. Never really had a serious problem on regular BTC-E and I traded there like crazy for a while (mostly converting BTC to LTC and vice-versa). Sent a few hundred bucks to the MT4 branch to test the waters (shorting BTC at times sounds great). They conveniently lost my litecoin and then ceased responding to my tickets. Also, there is some other fishy stuff going on with that company. Never had a problem with Coinbase after more than 100 transactions. I have 2FA and am the level II or III validated (the highest one). Actually, Coinbase the website goes down during the ultra high volume days. Sometimes during high volume they don't have BTC to buy because their hot wallet has been exhausted or their back-up source, Bitstamp, is out. No issues whatsoever selling BTC on any day (assuming the website is up). Note you can only sell up to 50 BTC a day unless you strike a deal (I don't think they would turn down a big shot). I have over 50 BTC and will just scale out or sell some elsewhere if there is a big spike or there is an unforseen negative and I need to dump.
One final point: Mt Gox claims that it was hacked. The coins were depleted from its cold storage. Mt Gox had a shady reputation for years; it is technically impossible that the coins were removed from true cold storage. In my opinion, Mt Gox is playing off the stupidity of the media and non-bitcoin people. Mt Gox had been mixing funds and operating fractional reserve until they kicked the can.
Come on now, a company ran from Slovenia registered in the UK and nobody knows their owners or officials? What could go wrong? Oh I am sorry, I have just realized I am talking about Bitstamp. BTC-E is ran from Bulgaria and the owners are from Russia, there is no fishy thing going on there.... I am sure they are completely safe... Or not: http://www.reddit.com/r/Bitcoin/comments/1rf0bh/warning_btce_selectively_scamming/
I don't deal with Bitstamp. I have never sent a foreign wire and I am in the US. Second Market and other domestic real exchanges (Coinbase is a meta exchange) are on the horizon. That said, Bitstamp has a good reputation.