Here's a listing of dog IQs by breed.  Dogs have undergone artificial  selection, so those selected for intelligence  (Border Collie) tend  to be very smart, while those selected only for appearance tend not to be so  smart.  It depends on what was being selected for.  A bloodhound typically has a  low dog IQ (doesn't respond well to commands) but has undergone intense  selection for smelling ability, so a bloodhound compensates for lack of  command response with a keen sense of smell.
Many have argued that mutts tend to be around average intelligence, depending on their  ancestry.  A mutt of high IQ ancestry (for example, a Border Collie,  German Shepherd & Golden Retriever mix) will be smart, but a mutt of low  IQ ancestry (for example, a Chow Chow, Basenji & Pekingese mix) will tend to  be dumb. 
A veterinarian reader tells me that most mutts today in urban areas are at least part pit bull terrier. Given that pit bulls have low dog IQs, this would mean that the average IQ of mutts would be on the lower end of the spectrum. (N.B. that pit bulls also have undergone recent heavy artificial selection for aggression, since they're often raised to fight.) 
It should also be noted that pariah dogs (mutts in the wild that have reverted back to wolf-like characteristics) tend to have low average dog IQs, as by dog IQ one means a dog's responsiveness to human commands.  Mutts, left alone for multiple generations, will develop pariah traits and eventually will lose traits of domestication, which means their dog IQ will drop. 
It should be noted, however, that what we think of as dog intelligence (response to commands) is not all that dog breeds underwent artificial selection for. For instance, breeds were selected for guarding, hunting, smelling, herding, appearance, etc., and each breed seems to have its own special abilities or appearance.  Breeds are important.  If dog breeds were to disappear and be transformed into a large class of mutts, we would lose the richness of canine biodiversity.
From The Intelligence of Dogs, by S. Coren
Ranks 1 to  10
Brightest Dogs
Understanding of New Commands: Less than  5 repetitions. 
Obey First Command: 95% of the time or better. 
Rank Breed 
1 Border Collie 
2 Poodle 
3 German Shepherd 
4  Golden Retriever 
5 Doberman Pinscher 
6 Shetland Sheepdog 
7  Labrador Retriever 
8 Papillon 
9 Rottweiler 
10 Australian  Cattle Dog 
Ranks 11 to 26
Excellent Working Dogs
Understanding  of New Commands: 5 to 15 repetitions. 
Obey First Command: 85% of  the time or better. 
Rank Breed 
11 Welsh Corgi (Pembroke)  
12 Miniature Schnauzer 
13 English Springer Spaniel 
14 Belgian  Tervuren 
15 Schipperke 
Belgian Sheepdog 
16 Collie
Keeshond  
17 German Shorthaired Pointer 
18 Flat-Coated Retriever
English  Cocker Spaniel
Standard Schnauzer 
19 Brittany 
20 Cocker Spaniel 
21  Weimaraner 
22 Belgian Malinois
Bernese Mountain Dog 
23  Pomeranian 
24 Irish Water Spaniel 
25 Vizsla 
26 Cardigan  Welsh Corgi 
Ranks 27 to 39
Above Average Working Dogs
Understanding  of New Commands: 15 to 25 repetitions. 
Obey First Command: 70% of  the time or better
Rank Breed 
27 Chesapeake Bay Retriever
Puli
Yorkshire Terrier 
28 Giant Schnauzer 
29 Airedale Terrier
Bouvier  Des Flandres 
30 Border Terrier
Briard 
31 Welsh Springer  Spaniel 
32 Manchester Terrier 
33 Samoyed 
34 Field Spaniel
Newfoundland
Australian Terrier
American Staffordshire Terrier
Gordon  Setter
Bearded Collie 
35 Cairn Terrier
Kerry Blue Terrier
Irish  Setter 
36 Norwegian Elkhound 
37 Affenpincher
Silky Terrier
Miniature Pinscher
English Setter
Pharaoh Hound
Clumber Spaniel  
38 Norwich Terrier 
39 Dalmatian 
Ranks 40 to  54
Average Working/Obedience Intelligence
Understanding  of New Commands: 25 to 40 repetitions. 
Obey First Command: 50% of the time or better. 
Rank Breed 
40  Soft-Coated Wheaten Terrier
Bedlington Terrier
Fox Terrier  (Smooth) 
41 Curly-Coated Retriever
Irish Wolfhound 
42 Kuvasz
Australian  Shepherd 
43 Saluki
Finnish Spitz
Pointer 
44 Cavalier King Charles  Spaniel
German Wirehaired Pointer
Black & Tan Coonhound
American  Water Spaniel 
45 Siberian Husky
Bichon Frise
English Toy  Spaniel 
46 Tibetan Spaniel
Foxhound (English)
Otterhound
Foxhound  (American)
Greyhound
Wirehaired Pointing Griffon 
47 West  Highland White Terrier
Scottish Deerhound 
48 Boxer 
Great Dane  
49 Dachshund
Stafforshire Bull Terrier 
50 Alaskan Malamute 
51 Whippet
Chinese  Shar-pei
Fox Terrier (Wire)  
52 Rhodesian Ridgeback 
53  Ibizan Hound
Welsh Terrier
Irish Terrier 
54 Boston Terrier
Akita  
Ranks 55 to 69
Fair Working/Obedience Intelligence
Understanding  of New Commands: 40 to 80 repetitions. 
Obey First Command: 30% of  the time or better. 
Rank Breed 
55 Skye Terrier 
56 Norfolk Terrier
Sealyham Terrier 
57 Pug 
58 French Bulldog 
59  Brussels Griffon
Maltese 
60 Italian Greyhound 
61 Chinese  Crested 
62 Dandie Dinmont Terrier
Petit Basset Griffon Vendeen 
Tibetan Terrier
Japanese Chin
Lakeland Terrier 
63 Old English  Sheepdog 
64 Great Pyrenees 
65 Scottish Terrier
Saint Bernard 
66  Bull Terrier 
67 Chihuahua 
68 Lhasa Apso 
69 Bullmastiff 
Ranks 70 to 79
Lowest Degree of Working/Obedience  Intelligence 
Understanding of New Commands: 80 to 100  repetitions or more. 
Obey First Command: 25% of the time or worse. 
Rank  Breed 
70 Shih Tzu 
71 Basset Hound 
72 Mastiff
Beagle 
73  Pekingese 
74 Bloodhound 
75 Borzoi 
76 Chow Chow 
77  Bulldog 
78 Basenji 
79 Afghan Hound
Further reading:
Eccles & Mount:  "Cross-breed Dogs Have More Health Problems than Purebred Dogs"  (For "Pariah Dogs," see entry here.)
Clark:  "Benefits of Hybrid Vigor Overstated"
 
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