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The crew version can be readily identified by the red capsule embroidery, however very accurate copies exist so close inspection is required. 

This is the common souvenir version og the Gemini 12 patch from A-B Emblems. Curiously the capsule is rendered in gold thread rather than red.

This reproduction was made by A-B Emblem in conjunction with Gene Dorr as a series of historically accurate crew patch reproductions. 

This patch was produced by CrewPatches.com in 2010 by A-B Emblem and faithfully reproduces the crew souvenir version. 

This is the version of the patch as worn by the crew. Unknown maker. 

This Apollo 13 patch is part of a set of modern reproduction Apollo patches produced by Cape Kennedy Medals. This patch is one of two versions of the Apollo 13 patch issued by Cape Kennedy Medals around the same time.

This Apollo 8 patch is part of a set of modern reproduction Apollo patches produced by Cape Kennedy Medals.  It is distinct in the use of non-serifed fonts in the crew member names.

Vintage reproduction. All horses are the same color and the rays of the sun are similar to the Lion Brothers Apollo 13 patch, and the moon appears like the A-B Emblem souvenir version.

While identical in appearance as the standard A-B Souvenir Apollo 13 patch, this patch was executed on a velvet backing instead of twill.

A moderately detailed variation of the Apollo 13 patch. The blue craters are distinctive as is the appearance of the Earth, which is white with brown spots. 

Bare cloth pack.

The Swissartex version is virtually identical to the A-B Emblem version.

I have never seen this particular line of Lion Brothers' Apollo emblems before. Marketed under their "Put-Ons" emblems line, Lion Brothers produced these Apollo 11, Apollo 12, Apollo 13 and Apollo 14 patches. There may be others, but these are the only one's I have seen. Had these not been in their original packaging, they would probably have not been able to be associated with Lion Brothers.

This is the version of the patch that was issued to the Apollo 13 crew, as well as some limited commercial release. Distinct crater detail, the black gaps in the rays of the sun and curved sun stitching pattern sets it apart from the Lion Brothers version. This was made by A-B Emblem.

The Swissartex Apollo 13 rendition is a plastic-backed, 4" patch. The stitching is a bit crude compared to the A-B Emblem version but has a unique lunar surface. Not a very common patch.

Part of the Willabee & Ward space emblem collection. The patch very closely resemble the A-B Emblem version.

A modern reproduction with a crude lunar surface and same colored horses. 4"

A-B Emblem's souviner version of the Apollo 13 patch. Curved stitching in the sun and the lightest colored horse appears a bit camel-like. 
Available with plastic and cloth-backed versions.

This is the most common 3" version of the Apollo 13 patch, produced by A-B Emblem.

Modern reproduction of original concept artwork for Apollo 8 by Al Stevens

This version lacks the red vertical line on the capsule.

Collected as a set with other 3" Mercury and Gemini patches. This set of patches, while at first glance appear to be regular A-B Emblem 3" souvenir versions, actually have some distinct oddities that set them apart. They all have cheesecloth backs.

Until the manufacturer is found, I will refer to this set as geminiunk1.

This variation has a maroon border.

Collected as a set with other 3" Mercury and Gemini patches. This set of patches, while at first glance appear to be regular A-B Emblem 3" souvenir versions, actually have some distinct oddities that set them apart. They all have cheesecloth backs.

Apollo 8 3" patch. This patch is unique in the stitching of the moon with an odd secondary crescent. Additionally, the names aren't as spread out along the flight path as other 3" Apollo 8 patches where the "B" in Borman and "S" in Anders are almost horizontal. Additionally, unlike most other 3" versions, this one is fully embroidered where others are twill.

This patch was collected in a set of other 3" patches, also dissimilar from "original" A-B Emblem issues. 

I am going to tag this collection with the "apollounk2" tag. Leading candidate is Cape Kennedy Medals based on the Apollo 17 patch in this set being a CKM patch.

Cape Kennedy Medals 3 1/4" Apollo 13. Packaged with collection that included Cape Kennedy Medals 3 1/4" Apollo 9 and Apollo 7. 

I am making a leap that this version is CKM due to the unique 3 1/4" size as well as the associate with at known CKM issue Apollo 9 in the same set. 

This patch is a member of a set of Apollo patches that, while closely resemble A-B Emblem's 3" set, have several identifiable differences that set them apart. 

This patch is a member of a set of Apollo patches that, while closely resemble A-B Emblem's 3" set, have several identifiable differences that set them apart. Plain packaging that says "Swiss Embroidered Emblem" for $0.98.

Similar to the A-B version but can be identified by the two colors of shading on the right side of the earth.
4"

Common souvenir version. 

A faithful reproduction by Eagle One Aerospace

This is a quality reproduction patch, that features a distinct silver flame on the torch. 

Common souvenir version.

This patch matches the crew-worn patch. It lacks the names of the astronauts that is common to souvenir versions.
Eagle One Aerospace version, can be identified by the point at the tip of the capsule.