There is not an exact translation for this term in Spanish (also in Italian I think). It refers to insects of the family of "Hemiptera" (same in Italian).

Some examples in this context (plant pest):

Green Bug = afide
Beet Bug = cimicetta della barbabietola
Cereal Bug = cimice di cereali
Potato Bug = cimicetta verda

Also look this italian page:
Petz.it -Insetti, farfalle e rane
... del subordine Heteroptera e Homoptera dell'ordine Hemiptera che include varie speci,
anche le cosiddette cimici acquatiche, le cicale, gli afidi ed altre. ...
www.petz.it/animali/insetti/file_principali/cimice.htm - 8k

My option is "cimici e afidi"

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Note added at 56 mins (2004-06-21 20:45:43 GMT)
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In this english page you will find a brief explanation about the actual identity of bugs (from a biological point of view):

True Bugs: Index of the Order Hemiptera
... Although the name bug has become loosly applied to most small insect-like ... Members
of the Order Hemiptera are characterized by sucking mouthparts that originate ...
www.insects.org/entophiles/hemiptera

And sorry, Hemiptera is an order not a family (I must refresh my memory).