Wouldn't it be secure enough just to park your coins at a reputable exchange such as Mt Gox?
NO of course not!
1. Mt Gox is not reputable at all (they have been hacked before). And having lotsa users or "being big" does NOT AT ALL automatically imply trustworthiness.
2. If they suddenly decide to shut down because they have enough funds and can retire, you're boned.
3. If one of their employees fucks up and causes a database crash or accidentally leaks some passwords or SQL credentials, you're boned.
4. If one of their employees turns out to be corrupt and disappears with your coins, you're boned.
5. When storing coins at Mt Gox, you don't own the private keys, and you have essentially no control over your coins whatsoever.
6. You're making yourself dependent on one random single foreign entity. You'd have to trust them completely, based on hardly anything.
One of the great things about Bitcoin is you don't
need to trust anybody. You need to trust mathematical principles.
I store my private keys in an encrypted archive (with a password that I will always easily remember, yet is impossible for anyone to guess or brute force) and I stored this archive on several places online and offline.
It doesn't get much safer than that.