Divine Intervention is fantastic for this. Remember to try to counter something juicy with this if you get the chance, or at least cancel an attack.
Playing a bit of armor can go a long way. Particularly Dragonscale Hauberk/Elemental Cloak against Lord of Fire. You can go all the way to 5+ armor and Veteran's Belt, but I think every build should run at least 3 armor for their mage.
With my Johktari Beastmaster, I put creatures in the way, and then try to maintain range 2. My opponent is typically hindered by my creatures, and I can use Tanglevine, Teleport, Mongoose Agility, and Surging Wave to help me maintain that range. Hindering + running away is a great way to slow down aggro.
For more passive builds, I like to use Block, but a defense like Deflection Bracers or Cobra Reflexes can help too.
Gorgon Archer supported by Teleport, Tanglevine, Teleport Trap, and other position control can really hurt many rushes. Once you've stacked enough Weak conditions on your opponent's creatures, they're not nearly as threatening.
Tough guards go a long way. Pet Timber Wolf and Iron Golem particularly come to mind, as they are relatively cheap for their stats, can go toe to toe with an aggressive mage, and are just solid options.
Agony can be huge, particularly on creatures with Doublestrike/Triplestrike/Sweeping. It's my favorite thing to play on an enemy Brogan or Lord of Fire.