I am unsure if this fits your idea of a "messaging" app, but you may want to look at Pushbullet for Android and its accompanying software for desktop, Apple phones and browsers.
What It Does
Being able to send and receive texts from computers (ideally both Windows & Mac) and phone (Android), e.g. cross-platform[.]
Currently a totally free service with no ads or in-app purchases that I am aware of (I don't own any Apple products).
Allows you to send in-app messages from your phone to "registered devices" (i.e. your computer or tablet).
Has a web interface at Pushbullet.com and a suite of software, apparently including a Mac desktop application and iPhone app.
The app doesn't require application opt-in for the receiver to receive messages using the app. In other words, I could send a text to any of my contacts with a cell number.
Utilizes your phone contacts so all your contacts are potentially available.
Have in-app "conversations" via email and (potentially) Hangouts/Facebook Chat contacts. It also supports WhatsApp, Telegram and Line according to this official blog post.
Allows you to recieve desktop notifications of incoming SMS, complete with partial or full text and contact information. MMS images are available in the desktop app interface (at least on Windows).
Allows you to send SMS from your desktop. You can choose
to respond to existing conversations or start new ones. No one needs to sign up for anything.
What's Not So Great
Currently the company behind Pushbullet isn't charging for any service and it has been this way since at least February 2015. But they are looking into "premium" services in the future (they are still a hip startup right now).
Web based exchange services which, among other things, means you need data plans and internet connections vs. plain-old SMS. I also had a small issues with disabled cookies and the website since I am privacy minded. The error message I received trying to log in was not helpful in explaining they needed to be enabled.
Apps are good but don't always feel as smooth as they should be. At a guess, I would say that both Android and desktop apps likely rely heavily on web technologies for display and interaction. As a personal preference, I like "native" apps compared to these kinds of cross-platform implementations.
On Android at least, the "app" isn't for direct SMS messaging. It is for sending messages to a device or using "conversations". Also, while standard XMPP chat contacts show up, it isn't really possible to have genuine XMPP conversations without a third party service (apparently).
Technical limitations or inconveniences. First, you need to install Android Wear to reply to Hangout Messages (you don't need an actual Android watch, just the software on your phone). More importantly, Mac and iPhone apps can only show notifications with each other (you can't see iPhone notifications on PC). This might be remedied with Windows 10 but nothing official yet.
Overall Thoughts
In an extremely limited field of programs that can bridge multiple platforms for messaging, Pushbullet does very well for me at the moment. Despite the limited compaints above, it stands head-and-shoulders above the competition in my opinion and I use it daily for cross-platform (Windows/Android) SMS and some messaging.
