What does really big mean ? In my case few hundred megabytes, up to 1 GB. Clearly, too much for email attachments - most providers caps them at around 5-15 MB.
Since we started doing screencasts, I need quite often to transfer work in progress - screen recordings, rendered MOV files between me and my co-host of the screencasts. I tried to upload the file to the company servers using VPN, but the speed of the secure uploads is nowhere close to being practical.
What works much better is free service called TransferBigFiles.com. There is no registration required, you just enter the recipient email and start upload. After uploading, the system sends you an email with link and the files stays up for few days, then is deleted. More than enough for the other party to download. With self-destruction, it is also less worries for you to remember clean-up.
The site also offers client for Windows, which I did not try (for obvious reasons) and shows ads selling software. These ads made me (strangely enough) more comfortable, as the intention of the creators is clear: attract traffic by free service and monetize on software sales / ads.
The other possible explanation is of course collecting of email adresses for not-so-noble purposes. I have no knowledge of this being the fact - since about a week and half of using the service, there was no spike in amount of spam. No spike meaning nothing beyond usual 300+ offers of 10 dollar Rolex, body enlargements, natural weight loss programs and help requests to transfer money from Nigeria and similars ...
All my emails are consolidated on Gmail, which does terrific job of weeding out 99.99% of these - so I do not really care so much if one more spammer gets my email. But if you are really worried, you can always get the 10 minute email, use it for receiving notifications and then email the link manually. The down side is that you must keep the 10 minute email alive until upload finishes - this may take few refreshes.