The eye arrangement can be a key factor when identifying spiders to family, and sometimes to genus, but are almost never useful in identifying to species. For identifying to species, spinnerets and leg details (especially first and 4th legs) are also useful. However, the best thing anyone can do is to get an extreme closeup of a male palp or the underside of a female abdomen, and have them examined by an expert.
Below are some of the best bugguide images of spider eye arrangements. (Some families are not represented yet) The black and white images created are from bugguide spider images and are looking into the spider's "face" (I plan to add a top view later). Because of this frontal view some eyes that are round may appear otherwise. Also keep in mind that eye arrangements may vary within the families, and the images below only represent a small portion of those spiders. Overall, 99% of all spiders have 8 eyes and of the remaining 1% nearly all have 6, but there are a few exceptions. Sometimes there can even be a varying number of eyes in the same spider family. For example, there are spiders in Cybaeidae that have eight eyes, six eyes, and two eyes. Those familes are followed with "(in part)" to show that not all spiders in that family have the same number of eyes.
Families with six-eyed spiders
  Anapidae (in part)
  Cybaeidae (in part-nearly all eight-eyed)
  Dictynidae (in part-nearly all eight-eyed)
  Diguetidae
  Dysderidae
  Leptonetidae (in part-nearly all six-eyed)
  Linyphiidae (in part-nearly all eight-eyed)
  Nesticidae (in part-nearly all eight-eyed)
  Ochryroceratidae
  Oonopidae (in part-nearly all six-eyed)
  Orsolobidae
  Pholcidae (in part)
  Scytodidae
  Segestriidae
  Sicariidae
  Telemidae (in part-nearly all six-eyed)
Families with two-eyed spiders
  Caponiidae
Families with four-eyed spiders
  Nesticidae (in part)
  Symphytognathidae
Families with no-eyed spiders
  Cybaeidae (in part-nearly all eight-eyed)
  Dictynidae (in part-nearly all eight-eyed)
  Leptonetidae (in part)
  Linyphiidae (in part-nearly all eight-eyed)
  Nesticidae (in part)
  Telemidae (in part-nearly all six-eyed)
  Theridiidae (in part)
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WOLF SPIDERS - Lycosidae (all eyes are round)
Unknown Genus

Hogna


Pardosa                            
Arctosa

   

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NURSERY WEB SPIDERS - Pisauridae
Dolomedes





Pisaurina





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HACKLEMESH WEAVERS - Amaurobiidae
Callobius


Amaurobius
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FUNNEL-WEB WEAVERS - Agelenidae
Agelenopsis


Tegenaria (all eyes are round)



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GHOST SPIDERS - Anyphaenidae
(this common name is not aknowledged by experts)
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SAC SPIDERS - Clubionidae
note, the first one is a Cheiacanthium which is still
usually placed in this family but some folks are saying it belongs in
another family. See Miturgidae.
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GROUND SPIDERS - Gnaphosidae
gnaphosids often have some eyes oval
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CYBAEIDS - Cybaeidae -
EIGHT, SIX or ZERO EYES
Cybaeus
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MESH WEB SPIDERS - Dictynidae
Dictyna
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SHEETWEB & DWARF SPIDERS - Linyphiidae
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ORB WEAVERS - Araneidae
dorsal aspect that araneid eyes are distinctive
Araneus


Neoscona                      
Larinioides

   
Argiope                                                      
Eriophora


   
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LONG-JAWED ORB WEAVERS - Tetragnathidae
Tetragnatha


Leucauge                      
Meta

   
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COBWEB WEAVERS - Theridiidae
Enoplognatha


Latrodectus


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CRAB SPIDERS - Thomisidae (see also
this article)
Misumena


Misumenoides                                                         Misumenops


       
Tmarus                                 Xysticus

   
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RUNNING CRAB SPIDERS - Philodromidae
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JUMPING SPIDERS - Salticidae
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LYNX SPIDERS - Oxyopidae
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FLATTIES - Selenopidae
(this common name is not aknowledged by experts)

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PIRATE SPIDERS - Mimetidae
try to get a better photo of a front leg
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PROWLING SPIDERS - Miturgidae
you have Cheiracanthium here (where it is currently, but
incorrectly placed in the World Spider Catalog) as well as in
Clubionidae. It will most likely end up in an independent family but a
nomenclatural tangle will have to be unraveled first since we can't
use the name Cheiracanthidae (it's already been used twice in other
groups!)
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WALL SPIDERS - Oecobiidae
your diagram needs a little work. You don't have the rows
separated enough and the posterior medians should be more oval. Also,
what makes this family look so distinctive is really the shape of the
whole carapace.
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CELLAR SPIDERS - Pholcidae -
EIGHT OR SIX EYES
diagram needs work. Lateral triagles should be distinctly
closer together than they are to the median pair, which should be
smaller. Also in Spermophora you've made the trangles too close
together.
Pholcus



Spermophora

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CREVICE WEAVERS - Filistatidae
while this photo does look like a filistatid, the eye
appearance is deceptive due to reflections. Get a better one (or check
out a preserved specimen) before doing a diagram. Levi in "Spiders &
Their Kin" has a top view diagram. Again, here the carapace shape is
pretty distinctive.
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TRAPDOOR SPIDERS - Ctenizidae
it is very atypical of the family.
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DYSDERIDS - Dysderidae -
SIX EYES
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RECLUSE SPIDERS - Sicariidae -
SIX EYES
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SPITTING SPIDERS - Scytodidae -
SIX EYES
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A special thank you to Jeff Hollenbeck and Rod Crawford for helping me with information for this article.