I'm looking to replace our Cisco 2900 router, and one of the choices is the MX84. My question is that can I use the AnyConnect VPN client for the MX84 or do I need a Cisco ASA?
Meraki MX routers do not support Cisco Anyconnect. If Anyconnect is a requirement I'm afraid you'll have to stick with Cisco branded routers.
Not currently supported.
This is likely due to the fact that AnyConnect establishes an IPSec Tunnel based on IKE v2 whereas the MX appliance (afaik) still uses IKE v1 for negotation.