Ideally, I would have like to had $10k set aside but is was more like $10.00
Our house is 60 years old and we've had to replace the furnace and AC in the first five years when my income has also taken a hit. We cut back in other areas including cars and savings - we had one car parked for two months until we could pay cash to fix it.
I think it depends on your tolerance for security/doing without. Some folks would not be able to sleep if buying a house or an unexpected expense meant cutting back on 401k contributions or not taking a "flying" vacation this year. Such folks should have that big e-fund. I'm glad we have our house and don't regret our decision to buy.
I had heard that one needs to budget about 2% of a home's value every year for furnace/AC replacements, a new roof, major appliance replacements, new water heaters, etc. This is above and beyond run of the mill repairs like fixing faucets and painting.