Written from my perspective and potentially varying in different countries but...
It is certainly possible to do a PhD without doing a MSc (I'm currently coming to the end of my PhD at a UK university and I applied straight from undergraduate). In my experience it is unusual though, possibly for good reason. You don't say why you don't want to do a Masters, but it's probably worth pointing out that if you are able to get a good MSc then it is likely to greatly help both your chances of getting a PhD and your academic development. The learning curve from undergraduate to PhD without a MSc can be a steep one, particularly in terms of managing your own time and activities.
If you have decent undergraduate grades (mine were ok but certainly nothing special), experience in a research environment and can convince whoever is making the decision about the application that you will be able to work well independently then I don't think there are any definite barriers against getting on a PhD. You may however find it difficult to compete with other applicants who have Masters degrees, since they have more definite proof of their ability to do independent, focussed research.
I'd suggest it's worth applying to PhD's if you feel that they are a good fit for both your interests and your experience, provided they don't absolutely require a MSc (for funding purposes etc). The worst that can happen is being turned down and you get some practice crafting applications. Obviously there is a time cost to this however so I'd advise being selective with your choices, only applying where you feel you have a real chance. This may also allow you to apply to some MSc programmes without having to worry too much about conflicting applications.
Hope that helps.