The real need for the var keyword was to support anonymous types in C# 3.0--which in turn were required to properly support LiNQ (Language Integrated Querying).
Without using var you could never do something like this:
var person = new { Name = "Peter", Age=4};
Which means that you couldn't execute execute the following linq query because you wouldn't know how to assign it to a variable:
[var/sometype] dogsFixedQuery = from myDog in kennel select new {dogName = myDog.FirstName + " " + myDog.OwnerLastName, myDog.IsNeutered, dogLocation = kennel.Address};
The utility of anonymous types will be more apparent if you start to create more complex linq queries with multiple levels of returns and joins.
The fact that you can use var in other ways to avoid typing out something like IEnumerable<Dictionary<List<string>,IOrderedCollection<DateTime>> myBadDesign = getBadDesignController().BadDesignResults("shoppingCart");
is just a side-effect/bonus in case you're a lazy typer =)
There are cons for readability if you start calling vars in disparate locations but if you're using var for a strong type and the compiler can determine the type of your variable than any reader should be able to determine it as well.