The number of possible Blimpy Burger combinations is:
2,147,483,648

How did we figure this out? There are four burger sizes, six cheeses (you can order all of them, some of them, or no cheese at all), four different bun types, nine different grilled items (you can get all, some, or none of them) and twelve different condiments (again you can get all, some, or none). So, according to noted Blimpy Addict Will G. -- roommate of former Blimpy staff -- the number of combinations is equal to:

6 9 12

(

)

(

)

(

)

4 x

6

x 4 x

9

x

12
c g n
c=0 g=0 n=0
("c" is for cheese, "g" is for grilled items, and "n" is for condiments) 
Using Matlab the following code will evaluate the expression:
>> v=0
>> for c=0:6
      for g=0:9
        for n=0:12
           s=4*(factorial(6)/factorial(6-c)*factorial(c)));
           t=4*(factorial(9)/factorial(9-g)*factorial(g)));
           u=(factorial(12)/factorial(12-n)*factorial(n)));
           v=v+(s*t*u);
         end
       end
     end
>>sym(v,'d')
ans=2,147,483,648