Step 1: Recall what cellulitis is.
Cellulitis is a spreading infection of the skin and the tissue just under it, usually showing up as redness, warmth, swelling and pain over the affected area, without a well-defined pus filled pocket.
Step 2: Recall the usual germs behind it.
Classic, non-purulent cellulitis, without an abscess, is most often caused by beta hemolytic streptococci, and among these, Streptococcus pyogenes, group A streptococcus, is the organism most commonly responsible. It spreads through tissue easily because it makes enzymes that break down the barriers between tissue planes.
Step 3: Rule out the other organisms listed.
Streptococcus faecalis, now usually called Enterococcus faecalis, is more linked to urinary tract and biliary infections, not typical skin cellulitis. Streptococcus viridans is part of the normal mouth flora and is better known as a cause of infective endocarditis and dental infections. Microaerophilic streptococci are associated with mixed, low oxygen wound infections and abscesses, such as in synergistic gangrene, rather than being the leading cause of ordinary cellulitis.
Step 4: Final Answer.
Streptococcus pyogenes remains the most common organism causing cellulitis.
\[ \boxed{\text{Streptococcus pyogenes}} \]