Does Bitcoin Core (bitcoind or bitcoin-cli) support HD wallet?
Can Bitcoin Core ...
Q1. create HD wallets?
Q2. import HD wallets from other wallet software?
Q3. watch HD wallet? (watch transaction or notify changes)
Update: As of bitcoin-core 13.0, core uses HD wallets by default.
create HD wallets?
No, but this is something being worked on.
import HD wallets from other wallet software?
No, HD wallets being transportable between software like this is unlikely due to the wide range of implementations. An Electrum seed is unlike an Armory seed is unlike a Bread wallet seed.
watch HD wallet? (watch transaction or notify changes)
Only if you
importaddress for a large number of future addresses which is cumbersome.
HD-wallets by default: Due to a backward-incompatible change in the wallet database, wallets created with version 0.16.0 will be rejected by previous versions. Also, version 0.16.0 will only create hierarchical deterministic (HD) wallets. Note that this only applies to new wallets; wallets made with previous versions will not be upgraded to be HD.