Yep. If you can prove you made the trip, claim it. So every receipt, every deposit.
I've only claimed the car costs in the last two years. All prior years I didn't bother but wow, it adds up. As said, for me, my kids are teens now and so my oldest has his own car, my youngest has friends who will drive so other than the odd instance of Mum's taxi for parties etc., my mileage is primarily household errands. Groceries, bank, gas.
Since I can go into town and get my stuff done with day care errands, I can write off a lot of the expenses of having a car.