With the poisson family the default link is the log, and in practice the major use of this family is to fit surrogate poisson log-linear models to frequency data, whose actual distribution is often multinomial. This is a large and important subject we will not discuss further here. It even forms a major part of the use of non-gaussian generalized models overall.
Occasionally genuinely poisson data arises in practice and in the past it was often analysed as gaussian data after either a log or a square-root transformation. As a graceful alternative to the latter, a poisson generalized linear model may be fitted as in the following example:
fmod <- glm(y ~ A+B+x, family=poisson(link=sqrt),
data=worm.counts)