Why use String.Format?

First, I find

string s = String.Format(
    "Your order {0} will be delivered on {1:yyyy-MM-dd}. Your total cost is {2:C}.",
    orderNumber,
    orderDeliveryDate,
    orderCost
);

far easier to read, write and maintain than

string s = "Your order " +
           orderNumber.ToString() +
           " will be delivered on " +
           orderDeliveryDate.ToString("yyyy-MM-dd") +
           "." +
           "Your total cost is " +
           orderCost.ToString("C") + 
           ".";

Look how much more maintainable the following is

string s = String.Format(
    "Year = {0:yyyy}, Month = {0:MM}, Day = {0:dd}",
    date
);

over the alternative where you'd have to repeat date three times.

Second, the format specifiers that String.Format provides give you great flexibility over the output of the string in a way that is easier to read, write and maintain than just using plain old concatenation. Additionally, it's easier to get culture concerns right with String.Format.

Third, when performance does matter, String.Format will outperform concatenation. Behind the scenes it uses a StringBuilder and avoids the Schlemiel the Painter problem.

I can see a number of reasons:

Readability

string s = string.Format("Hey, {0} it is the {1}st day of {2}.  I feel {3}!", _name, _day, _month, _feeling);

vs:

string s = "Hey," + _name + " it is the " + _day + "st day of " + _month + ".  I feel " + feeling + "!";

Format Specifiers (and this includes the fact you can write custom formatters)

string s = string.Format("Invoice number: {0:0000}", _invoiceNum);

vs:

string s = "Invoice Number = " + ("0000" + _invoiceNum).Substr(..... /*can't even be bothered to type it*/)

String Template Persistence

What if I want to store string templates in the database? With string formatting:

_id         _translation
  1         Welcome {0} to {1}.  Today is {2}.
  2         You have {0} products in your basket.
  3         Thank-you for your order.  Your {0} will arrive in {1} working days.

vs:

_id         _translation
  1         Welcome
  2         to
  3         .  Today is
  4         . 
  5         You have
  6         products in your basket.
  7         Someone
  8         just shoot
  9         the developer.

Besides being a bit easier to read and adding a few more operators, it's also beneficial if your application is internationalized. A lot of times the variables are numbers or key words which will be in a different order for different languages. By using String.Format, your code can remain unchanged while different strings will go into resource files. So, the code would end up being

String.Format(resource.GetString("MyResourceString"), str1, str2, str3);

While your resource strings end up being

English: "blah blah {0} blah blah {1} blah {2}"

Russian: "{0} blet blet blet {2} blet {1}"

Where Russian may have different rules on how things get addressed so the order is different or sentence structure is different.