Web clients is a quite new thing to be honest. Years ago there were a few companies who tried to create web client as the new thing but failed in doing so. This is mostly due the fact that back then the frameworks as we know them now didn't exist. This resulted in every action being a new page and a new call. Companies then left the idea and went for hard clients (such as vSphere Client as an example here). Keep in mind that this means another service (or multiple) needs to be monitored and up and running all the time.
Over time things have changed and the 'web' improved a lot. Things got more fluent and 'snappy' with the perfect example being Facebook, LinkedIn and Twitter (social media). While these aren't apps they are a perfect example how smooth things can be.
VMware felt the need to try it again but made the initial wrong choice of going for flash compared to HTML5, javascript & CSS (such as AngularJS, bootstrap, ReactJS,... plenty of choice there is). They failed by doing so and the first few web clients were unusable and sadly due to this many people still refuse to use the web client. However VMware made the wise choice to switch to HTML5 thanks to the success of their fling. If you look at how good the web client has become in 6.5 it's a perfect example on how to do it correctly. The bigger problem I see with the way VMware handled things is the full redesign of their client. I've spoken quite some people about it (in regards to getting feedback how we should do it

) and many feel they are 'lost' and the learning curve is 'high'. Of course this is also due to the fact that the fat client has been along for quite a while so this is just a matter of time.
While I can't say where Veeam is going I can give my personal opinion on how things are changing.
The first example (as Craig mentioned) is the Veeam Availability Console. This is a full HTML5 management web interface which comes with a RESTful API meaning you can make your own interface if you don't like ours but it also allows you to integrate certain aspects within your own portals.
The second example is the upcoming Veeam Backup for Office 365 1.5 release (currently in BETA) which has exactly the same options. It comes with a RESTful API making sure you can do pretty much all the calls you can do via the fat client via REST. This allows us to integrate with portals or create an own design (which I am working on as an example - keep an eye at
https://github.com/nielsengelen/vbo365).
For those who are saying 'no don't do it' in this thread; my question is simple. Why wouldn't we open up with a REST api allowing people to create a HTML5 interface? Is this due to the VMware example?
For those who says 'yes go for it': which are things you would like to see in it? Keep in mind that doing a full switch with 1 release isn't feasible so this would be step by step.
Also I am not a developer nor in product management but I am all up for the idea of 'Veeam flings' to help demands.