Not with the same enthusiasm as Intel: Server motherboards, pretty much regardless of vendor, will have an IPMI-or-more implementation of...widely varying...quaility; but "Intel AMT" is widespread across desktops and laptops(it's mostly a 'business' feature, so it's often gimped or disabled in consumer gear; but that still means that the capability is widely present in non-server chipsets.)
This isn't so much a matter of virtue on AMD's part; but of tardiness: they've thrown in their lot with technology based on the 'TrustZone' stuff traditionally found in ARM cores; and are making a go of rolling out some similar capabilities. They just don't have much leverage in the business-boxes market.
Speaking from my limited experience with Intel AMT(we don't use it at work; but some of the hardware we have is capable of it so we've tested it), one can see why it would be an attractive IT management feature; but one can also see why it would make people nervous.
The capabilities depend both on firmware and on hardware(minor version bumps are usually doable with firmware; major version bumps occur when a new chipset is rolled out, wikipedia has a roundup of the versions).
At least with reasonably new AMT, the capabilities are quite sophisticated. The ARC(or, amusingly enough, SPARC in newer versions; who would have thought that Intel is probably one of the world's leading SPARC vendors, by volume?) core remains active at all times when power is available(so all the time for desktops, most of the time for laptops) and has its own IP stack, so you can talk to it even if the main computer is powered off, has no OS, or even has all the RAM pulled. The AMT device can also(sometimes this requires cooperation with the guest OS, exactly when it does and doesn't gets really tedious really quickly) establish VPN links back to HQ even if the device is on an external network.
One particularly impressive(if, equally, disconcerting) capability is the ability to act as an IP KVM: so long as the host computer is using intel graphics, you can connect through AMT and view the screen(including POST and boot stuff, prior to the OS loading) and use a virtual keyboard and mouse for remote control, as well as mounting ISOs over the network. It's based on a slightly oddball implementation of VNC; but it's a version of VNC that is baked into the hardware and works regardless of the state of the host OS.
The capabilities are pretty cute; but, as always, 'pretty useful for the IT guys' and 'zOMG rootkit from hell!' is less a technical difference than a difference in ownership and motive.