There are 2 solutions:
Solution #1:
        <MenuItem Mixed Fruit 215>
        <MenuItem Hot Wings 355>
        <MenuItem Hot Wings 355>
        <MenuItem Sampler Plate 580>
Solution #2:
        <MenuItem Mixed Fruit 215>
        <MenuItem Mixed Fruit 215>
        <MenuItem Mixed Fruit 215>
        <MenuItem Mixed Fruit 215>
        <MenuItem Mixed Fruit 215>
        <MenuItem Mixed Fruit 215>
        <MenuItem Mixed Fruit 215>

This isn't "as fast as possible" to be sure, but it should be a general solution.

#!/usr/bin/env python

"""Attempt to solve XKCD from July 9 2007"""

#All monetary values are in pennies to avoid floating point errors
# (Yea, I could use decimal.Decimal but it's SLOW!)

import operator

class MenuItem:
    def __init__(self, name, price):
        self.name = name
        self.price = price
    def __add__(self, other):
        if hasattr(other,"name") and hasattr(other,"price"):
            #This is a MenuItem
            return self.price + other.price
        else:
            return self.price + other
    def __repr__(self):
        return "" % (self.name,self.price)

appetizers = ( MenuItem("Mixed Fruit",      215),
               MenuItem("French Fries",     275),
               MenuItem("Side Salad",       335),
               MenuItem("Hot Wings",        355),
               MenuItem("Mozarella Sticks", 420),
               MenuItem("Sampler Plate",    580))

target_price = 1505

def find_solutions(stack=[],solutions=set()):
    """Find combinations of appetizers that equal target_price"""
    #Find if initial stack equals target_price
    stack_price = sum([x.price for x in stack])
    if stack_price == target_price:
        #print("Found a solution!!! " + str(stack) + " == " + str(target_price))
        stack.sort(key=operator.attrgetter('price'))
        solutions.add(tuple(stack))
    elif stack_price > target_price:
        #No solutions for this stack
        return set()
    #Recurse for each item
    for item in appetizers:
        find_solutions(stack + [item])
    return solutions

if __name__ == "__main__":
    solutions = find_solutions()
    print "There are %d solutions:" % (len(solutions))
    solution_num = 1
    for solution in solutions:
        print "Solution #%d:" % (solution_num)
        for item in solution:
            print "\t%s" % item
        solution_num += 1

Update July 10: Visitor wac pointed out that my program is pretty inefficient. I agree - I did it really quick on my lunch break yesterday. For order values above $20 it becomes an intractable solution pretty quick. Here is a much more efficient solution that implements value caching (at the cost of requiring more memory than the previous solution):

#!/usr/bin/env python

"""Attempt to solve XKCD from July 9 2007

This is a new version that uses a cache for calculations
"""

#All monetary values are in pennies to avoid floating point errors
# (Yea, I could use decimal.Decimal but it's SLOW!)

import operator
import sys

class MenuItem:
    def __init__(self, name, price):
        self.name = name
        self.price = price
    def __add__(self, other):
        if hasattr(other,"name") and hasattr(other,"price"):
            #This is a MenuItem
            return self.price + other.price
        else:
            return self.price + other
    def __repr__(self):
        return "" % (self.name,self.price)

appetizers = ( MenuItem("Mixed Fruit",      215),
               MenuItem("French Fries",     275),
               MenuItem("Side Salad",       335),
               MenuItem("Hot Wings",        355),
               MenuItem("Mozarella Sticks", 420),
               MenuItem("Sampler Plate",    580))

class OrderCache:
    """a cache of all the possible variations of an order for a given price"""
    def __init__(self):
        self.cache = {0:set([()])} # price -> set([(item1,item2 ...), ...])
    def derrive_order(self, price):
        "Return all combinations for a given price"
        try:
            return self.cache[price]
        except KeyError:
            orders = set()
            for item in appetizers:
                if price - item.price >= 0:
                    for order in self.derrive_order(price - item.price):
                        new_order = list(order) + [item]
                        new_order.sort(key=operator.attrgetter('price'))
                        orders.add(tuple(new_order))
            self.cache[price] = orders
            return orders

if __name__ == "__main__":
    if len(sys.argv) == 2:
        target_price = int(sys.argv[1])
    else:
        target_price = 1505
    order_cache = OrderCache()
    solutions = order_cache.derrive_order(target_price)
    print "There are %d solutions:" % (len(solutions))
    solution_num = 1
    for solution in solutions:
        print "Solution #%d:" % (solution_num)
        for item in solution:
            print "\t%s" % item
        solution_num += 1

With the improved version I can calculate order values up to $75 in under a minute. That's interesting in and of itself really, because although the second algorithm is much more efficient it would still be practically impossible to calculate an order value of $1000. That's the nature of NP problems for you.

Yea, you're probably saying to yourself, "WTF IS THAT?"

It's LOLPython, the geekiest, funniest thing I've seen all week!

The LOLPython interpreter translates a variation of LOLCode into standard python. LOLCode itself is pretty neat, but because LOLPython is based on Python, it automatically inherits all of the Python library too. Here's the above code after translation:

from time import localtime as TIMEZOR
if __name__ == '__main__' :
    print 'YOUZ GOT CHEEZBURGERS?'
    CATURDAY = 5
    TODAYZ = TIMEZOR ()[ 6 ]
    YOUGOTZ = raw_input ()
    if YOUGOTZ . lower ()== 'yes' :
        if TODAYZ == CATURDAY :
            MYLOOPZ = 3
            while 1:
                print 'TODAYZ CATURDAY! I GETZ ALL YOUS CHEEZBURGERS!'
                MYLOOPZ -= 1
                if MYLOOPZ <= 0 :
                    break
        else :
            print 'O RLY? CAN I HAS YOUS CHEEZBURGER?'
    else :
        print 'I SAW WHAT YOU DID, YOU ATE MY CHEEZBURGERS!'

bin = ['01011001','01001111','01010101',
       '01001110','01000101','01010010','01000100']
for b in bin:
   print chr(int(b,2)),

I Love comics that are made just for me.