I've had a pleasant experience with Dropbox, not much hassle and okay speeds. Most of my friends use Dropbox, one also uses Google to share stuff, as it integrates well with their Android devices. There are also backup services offered by antivirus software companies like F-Secure, which I would assume are somewhat trustworthy and long-lived, but the space offered is rather limited.
I would avoid places like Mediafire or Minus that concentrate on sharing the files, as they may get targeted in anti-piracy action.
It's not tinfoil-hattery to assume your data will be exposed and mined, either by accident/negligence (Sony) or on purpose (Facebook), so encrypt anything that is personal BEFORE sending it out into the wild. The more prevalent cloud services become, the more likely it is someone will want to get their hands on those vast data vaults. With modern processing power and apps like TrueCrypt the encryption happens seamlessly, and you can sleep easy.
US authorities are notorious for snooping, but even a friendly, harmless place like Sweden actively monitors not just offenders, but ALL traffic
. "Be vigilant."