The Baltimore Classification System for viruses is named after David Baltimore, who proposed it

The Baltimore Classification System for viruses is named after its developer David Baltimore. David Baltimore (born 1938 in New York) is an American biologist, who won the Nobel Prize in Physiology and Medicine in 1975 together with co-recipients Renato Dulbecco and Howard Martin Temin for their discoveries concerning the interaction between tumor viruses and the genetic material of the cell [1].

The Baltimore classification accounts for the different mechanisms of viral genome replication. This system is schematically organized via the relationship between the viral genome and the messenger RNA  (mRNA), which is critical in the translation during expression of the viral genome [2-4]. The following presentation of the Baltimore classification is based on the system and virus examples given in Bruce Voyles' book (first six classes) [4] and on web-based resources [2,3]:

• Class I viruses, double-stranded DNA genomes: the genome is double-stranded DNA, so  mRNA is synthesized in the normal fashion using negative-strand DNA as a template. Examples: adenovirus, hepatitis B virus, cauliflower mosaic virus.
• Class II viruses, single-stranded DNA genones: the genome is single-stranded DNA. At the time this scheme was proposed, only positive-strand Class II viruses were known, but negative-stand viruses have since been found. They are now designated Class IIa and Class IIb, respectively. Examples: parvovirus, maize streak virus.
• Class III viruses, double-stranded RNA genomes: the genome is double-stranded RNA, one strand of which is therefore equivalent to mRNA. These viruses have segmented genomes. Each genome is transcribed separately to produce monocistronic mRNAs. Examples: reovirus, rotavirus.
• Class IV viruses, positive-strand RNA genomes: the genome is single-stranded RNA that can serve as mRNA directly, so these are positive-strand viruses. There are two subclasses (IVa and IVb) based on differences in mechanisms for expression and replication of the genome in these viruses. Examples: poliovirus, hepatitis A virus, coxsackievirus, tobacco mosaic virus.
• Class V viruses, negative-strand RNA genomes: the genome is single-stranded RNA that cannot serve directly as mRNA, but is instead the template for the synthesis of viral mRNA. Since the genome is complementary to the viral mRNAs, these are negative-strand viruses. Class Va and Vb viruses are also distinguished by differences in the mechanism used in expression and replication of their genomes. Examples: rabies virus, mumps virus, measles virus, influenza A and B, Lassa virus.
• Class VI viruses, retroviruses, also termed RNA-tumor viruses: the genome is positive-strand RNA but its expression and replication require synthesis of a double-stranded DNA molecule (reverse transcription). Example: human immunodeficiency virus (HIV).
• Class VII viruses: double-stranded DNA with RNA intermediate: This group of viruses relies on reverse transcription, but unlike the Class VI retroviruses, the transcription occurs inside the virus particle on maturation. On infection of a new cell, the first event to occur is repair of gapped genome, followed by transcription. Example: hepadnaviruses.

References and suggested reading
[1] David Baltimore, 1975 Nobel Laureate in Medicine:  nobelprizes.com/nobel/medicine/1975a.html.
[2] ViralZone: The Baltimore classification clusters viruses into families depending on their type of genome [expasy.org/viralzone/all_by_species/254.html].
[3] Virology Tutorial: Classification of Viruses [www.nlv.ch/Virologytutorials/Classification.htm].
[4] Bruce A. Voyles: The Biology of Viruses. WCB/McGraw-Hill, Salem, MA, 1993; pages 29-32.