I have a cross-sectional database (n=500) and I am exploring the association between a number of factors (5) and one outcome, the number of accesses to a service (count of data). I was wondering if the use of Poisson regression is correct in this case. I have used Poisson regression in few occasions with longitudinal (and panel) data while I only used the negative binomial regression in the only occasion I explored an association cross-sectionally where the outcome was a count of events (but in that case the data was extremely skewed and I went for nbr rather than Poisson). Is then ok to use simply Poisson in this case (as I do not have skewed data) with cross-sectional data? I would simply use the beta coefficient to describe the association rather than calculate the RR, is this the right approach?
Yes, ordinary Poisson regression is fine for use with cross-sectional data. If you wanted to use Poisson regression for longitudinal data that you are used to, you would typically use a Poisson mixed model or a generalized estimating equations to account for dependency/correlation among the observations. If you are have cross-sectional independent observational count data though, Poisson regression is a good starting point. Of course, any good model will require that you validate the fit of the model using the usual diagnostic checks. If you find your model doesn't fit well after examining the fit and diagnostics, you will likely need to use more complex models, such as a negative binomial regression model.
Also, in one of your comments, you asked about whether or not you should use the "Robust" option when fitting your model. Generally speaking it's nearly always a good idea to use this option. See here for a full discussion: When to use robust standard errors in Poisson regression?.