There was at least one site that did this I remember.
http://bitping.net will send you email notifications on any transactions to/from a bitcoin address.
you can set up free transaction alerts for any bitcoin address here
As of October 2015, the only services that still seem to offer email notifications (for free) for transactions on an address (for which they don't need the private key) appear to be:
http://blockchain.info/wallet with the option to add a wallet as watch-only. It doesn't seem 100% reliable (it missed a few transactions initially), but now it seems to work and gives a notification pretty much instantly.
http://blockonomics.co with which I had a temporary problem with validating the confirmation email, but seems to work otherwise. Notification emails arrive a bit later (maybe they wait for the transaction to be confirmed or something like that?).
- Easy setup.
- Sends crafted notifications.
- Watch-only address monitoring service. Works without the private key.
You can add that address to blockchain.info/wallet, as watch-only if you prefer, and enable email notifications.
(didn't try that myself with watch-only addresses, so this might fail)
- unlimited notifications
- very quick response time
Try http://blockonomics.co . I use it get email notifications and check balance, sends a nice formatted email
https://cryptocurrencyalerting.com might be what you're looking for. They will monitor a BTC or ETH wallet address and notify you whenever a transaction occurs. Supports email/sms/telegram/slack/etc. ERC-20 coins are accepted. (Disclosure: I am affiliated with the creators of this service)