Historically RSA keys have been used with key sizes ranging from 512 bit to 4096 bit.
Keys with 512 bit have first been practically broken in 1999, keys with 768 bit in 2010. It is believed that a powerful adversary can break 1024 bit, however this has not been publicly demonstrated.
Modern recommendations are therefore to use a minimum key size of 2048 bit with RSA. Keys with 4096 bit are also a common choice, keys larger than 4096 bit are often unsupported, as very large keys can lead to denial of service issues.
Theoretically RSA allows keys of arbitrary size, including key sizes that are not aligned to byte sizes (e.g. 2049 bit keys, which is not a multiple of 8). Such unusual key sizes may lead to compatibility issues, as implementations may not have been tested with such keys. The majority of implementations default to key size choices that are multiples of 1024. It is recommended to use a common key size like 2048, 3072 or 4096 bit.