It is permissible.
However, it should not negatively affect people who are financially dependent on you (that is, you should not voluntarily impose poverty on financial dependents such as a wife or children), and you also should not put yourself in a situation where you are financially dependent on people (for instance, taking state benefits by choice).
Also you should not make this into a religious requirement or ideal; rather just say to others and to yourself that it is your preference.
Basically you can live according to any lifestyle you want, as long as it does not involve anything harmful or forbidden, and as long as you don't require it for others or become arrogant about it.
People have different personal and spiritual needs and perhaps some people do better spiritually with a simple lifestyle. However, it is good to remember that the Prophet (S) was both rich and poor, and his example was of being actively involved in society - including financial aspects - while maintaining spirituality.
Also, there is an advantage to having wealth, if you are able to use it to assist the less fortunate or use it in the performance of religious acts (such as performing the hajj). For instance, Imam Hasan (A) would not have been known for his generosity if he did not have any wealth to give.
Overall, I think it is fair to say that, as an ummah, the Muslim world today is in greater need of overcoming mass poverty, than encouraging voluntary poverty. (Of course this is a complicated issue since one of the main problems in the Muslim world is the unequal distribution and misuse of wealth, not actual lack of wealth, and not all Muslim areas are poor, but it cannot be denied that poverty is a debilitating problem for too many Muslims. This is a social problem not an individual problem, but just putting it out there.)
That being said, the Prophetic teachings discourage an overfocus on or overindulgence in wealth; rather, they encourage people to follow the path of moderation.
In any case, none of us is the Prophet (S), so we have to make the best decisions for our own lives in the matters which are left to our own choice.