The Artists of Holmes Basic

Holmes Basic set and rulebook (page #s refer to 1st edition unless noted)

No artists are credited in the rulebook, but at least three contribute. The majority of the work is by David C. Sutherland III (aka DCSIII), with  David Trampier (aka DAT) and Tom Wham contributing three pieces each

Wizard and Warrior versus Red Dragon (cover) - Sutherland

Adventurers versus Orcs (title page) - Sutherland (as SUTHERLAND III) - see image to right

Lizardman on Lizard Mount (pg 3) - Sutherland

Alignment Diagram (pg 8) - unknown. The version in the 1st edition is different from that in 2nd-3rd editions.

Web Spell (pg 16) - Trampier (as DA TRAMPIER)

Warrior versus Minotaur (pg 16) - Trampier

Dwarves (pg 25) - Sutherland

Wizard and Gnolls (pg 27) - Wham (as TW)

Gray Ooze (pg 27; 1st edition only) - unknown, possibly Sutherland

Warriors versus Harpies (pg 28; 2nd edition only) - Sutherland

Warrior versus Hydra (pg 29; 2nd edition only) - Sutherland

Manticore (pg 30) - Trampier (as DAT)

Purple Worm (pg 31; 1st edition only) - Sutherland - see image to right

Skeleton (pg 32; 2nd edition only) - Sutherland

Coins & Jewelry (pg 33; 1st edition only) - Sutherland - seem image to right

Sword with Jeweled Scabbard (pg 35) - Wham*
*Thanks to Rhuvein on Dragonsfoot; he heard directly from Tom that he drew this sword.

Wizard's Treasure (pg 37) - Sutherland

Sample Cross Section of Levels aka Skull Mountain (pg 38) - Wham. See this post.

Sample Dungeon Map (pg 41) - original design by J. Eric Holmes; published version by unknown, possibly Sutherland

Warriors versus Crypt Skeletons (pg 44) - Sutherland

Holmes Basic set and rulebook - UK version
John Blanche - front cover

Fangorn (aka Chris Baker) - interiors, many are re-drawings of the originals

Monster & Treasure Assortment - Set I
David C. Sutherland III - cover and interior illustrations

B1 In Search of the Unknown (monochrome)
David C. Sutherland III - cover (as DIS), back cover, all interiors (as DCS or SUTHERLAND III)

David Trampier - cover (as DAT)

The cover is credited to both artists. See here for Trampier's original version.

B2 Keep on the Borderlands (1st print - Wizard Logo; cover mentions AD&D)
Jim Roslof - front cover, owlbear on title page (as ROSLOF) - (see here for a partial list of Roslof TSR illustrations)

Erol Otus (EO) - back cover, four interior illustrations (as EO)

David S. Laforce - two thematically linked interior illustrations on page 7 (as DSL)

B2 Keep on the Borderlands (2nd print - Wizard Logo; cover does not mention AD&D)
Two pictures were added to this print in place of the section on using the module with AD&D

Dave Trampier - intertwining snakes (page 5). Uncredited, but the style is very similar to his other work. See this post at The Cryptic Archivist.

David C. Sutherland III - dragon (page 6). See picture to the right.
This dragon originally appeared in that last issue of Strategic Review (#7, April 1976, page 11) to advertise the upcoming debut of Dragon magazine (thanks to paleologos on Dragonsfoot for this info). It was then used in the 2nd print B2, along with the snakes illustration, to fill in for deleted text referring to AD&D. It was not included in the revised Moldvay version of B2, but was instead used in the Moldvay version of B1.

Chapel of Silence in Dragon # 50
Roger Raupp - module cover illustration

The Creature of Rhyl in Dragon #55
Harry Quinn - module cover illustration and five interior illustrations

Boinger & Zereth stories by Dr. Holmes
Were-shark (Alarums & Excursions #13, July 1976) - one illo by Chris Holmes

The Adventure of the Giant Chameleon (Alarums & Excursions # 14, Aug 1976) - two illos by Chris Holmes

Trollshead (THE DRAGON #31, Nov 1979) - illustration by Chris Holmes

The Sorcerer's Jewel (DRAGON #46, Feb 1981) - illustrations by Jim Roslof

In the Bag (DRAGON #58, Feb 1982) - illustrations by Donna Barr

THE MAZE OF PERIL (1986) - cover Dan Day, frontispiece Gregorio Montejo.

Other articles in Dragon magazine by Dr. Holmes
Lovecraftian Mythos in D&D (THE DRAGON #12, Feb 78) - "From the Sorceror's Scroll" illustration, artist unknown

Lost Civilizations: Fantasy Supplement for Source of the Nile (THE DRAGON #12, Apr 1979) - title illustration by Chris Holmes

Selected Images:

Adventurers versus Orcs by DCSIII from the title page of the rulebook (Click on picture for a larger view).
The trio appears to be the original three classes: Fighting Man, Magic-User, Cleric (wielding a mace).
Note the small Gargoyle on top of the pillar.

Purple Worm by DCSIII from page 32 of the 1st edition rulebook

Coins & Jewelry by DCSIII from page 33 of the 1st edition rulebook

     Advertisement from Strategic Review #7, with Dragon by DCS later used in B1 and B2