There are tilting trains on the classic Norte network, eg Madrid-Irun/Bilbao.
They run onto the Burgos-Madrid HSL at 250km/h.
The trains are Renfe class 120/121 built by CAF/Alstom, and are dual gauge/power supply.
The same trains run from Irun to Barcelona I believe.
There are also non-tilt versions of the same train, running eg Madrid-Toledo/Salamanca via the HSL.
There's also the Renfe class 130/730 which is a high-speed tilting train from Talgo.
The class 730 also has a diesel power pack to run on non-electrified routes.
It is used on Galicia-Madrid services via Zamora, though much of its tilting route has been eliminated by the new Zamora-Ourense HSL.
Generally, HS services from Madrid to Barcelona/Valencia/Malaga/Seville are non-tilt AVE trains, but occasionally a tilting train will turn up when the train runs through to the classic network (eg perhaps Madrid-Cordoba-Cadiz/Algeciras).
A few trains also run across Madrid now that there is a standard-gauge route under the city (eg Alacant-Madrid Chamartin-Santander/Leon).