Half year ago I have purchased my two HP printers (all-in-one devices), that utilizes HP ePrint solution. It was HP 8500A and HP 1536 MFP. There are many reviews about each of this printers, so I'll focus in my experience with HP ePrint solution only.
Here is the list of things, that I found and that you should consider, if purchasing HE ePrint-enabled printer:
1. Perfectly working, registered device can at some point unregister itself from the service. Suddenly you won't be able to send any document to it and when you login to HP ePrint portal you'll be surprised (or not) to find out, that it is gone. Just like that.
2. You must manually re-register your device and you must... start using a brand new email for it. For the next half of year your email address used by any device in HP ePrint service (including removed devices) will be "locked" before re-using it with any other device. HP Support has confirmed, that once email address is assigned to any printer, it cannot be removed or assigned to another, even if previous one was removed.
3. There is an absolute lack for two-side printing in HP ePrint. You can have perfectly duplex printer, configured to always print all documents two-sided and still are docs emailed to this printer will be printed one-sided. A lot of paper is lost because of that. This is not the only problem with configuration, as you actually cannot control anything about how emailed documents are printed.
4. There are sometimes strange problems with job confirmation. For example, you can receive confirmation email, that your document was printed, while nothing is actually printed out.
5. There's also a very short timeout window for receiving online job. Your printer may only be "busy" for about 30-60 seconds (printing some other document, starting up etc.) and your mailbox will immediately be flooded with stupid email only to let you know, that your device is busy and will print your document "a bit" later. Taking delays between checking inbox / delivering emails in many mail services and for many times I received "delay" email in the same time as "confirmation" email, that my document was actually printed out.
6. HP ePrint implementation differs among printers. I've sent exactly the same text image as email attachment to both my HP ePrint-enabled printers and received different results. HP 1536 printed entire image on entire page (with correct aspect ratio) while HP 8500A printed it only on 1/4 of the page, cut on top and bottom margin, making image nearly unusable.
I'm quite satisfied with HP ePrint service, even though above glitches may be little bothering. If you want to use this technology as remote printing solution, then you have to carefully test your device and consider, if above problems will be acceptable by you.
If you have a computer that is turned on and connected to the Internet for 24 hours, you may consider connecting your printer to it and installing Chrome browser on it. This solution gives you very similar results, using Google Cloud Print technology, without need of buying new device. Having an ability to control, how your document or image is printed via cloud printing, is an additional big plus, when considering solutions alternative to HP ePrint solutions.