Plasmids are autonomously replicating circular extra-chromosomal DNA. They are the standard cloning vectors and the ones most commonly used.  Most general plasmids may be used to clone DNA inserts of up to 15 kb in size.  One of the earliest commonly used cloning vectors is the pBR322 plasmid.  Other cloning vectors include the pUC series of plasmids, and a large number of different cloning plasmid vectors are available.  Many plasmids have high copy numbers, for example, pUC19 has a copy number of 500-700 copies per cell, and high copy number is useful as it produces greater yield of recombinant plasmid for subsequent manipulation. However low-copy-number plasmids may be preferably used in certain circumstances, for example, when the protein from the cloned gene is toxic to the cells.
Some plasmids contain an M13 bacteriophage origin of replication and may be used to generate single-stranded DNA.  These are called phagemids, and examples are the pBluescript series of cloning vectors.