Sure! It is allowed for lay people, as long as they observe [the five precepts][1] and [virtue (sila)][2], which includes [Right Livelihood (samma ajivo)][3]. Please also see [this answer][4].

The [Vanijja Sutta][5] states:

> "Monks, a lay follower should not engage in five types of business.
> Which five? Business in weapons, business in human beings, business in
> meat, business in intoxicants, and business in poison.
> 
> "These are the five types of business that a lay follower should not
> engage in."

The [Sigalovada Sutta][6] states:

> The wise endowed with virtue    
> Shine forth like a burning fire,    
> **Gathering wealth as bees do honey    
> And heaping it up like an ant hill.    
> Once wealth is accumulated,    
> Family and household life may follow.**
> 
> By dividing wealth into four parts,    
> True friendships are bound;    
> One part should be enjoyed;    
> **Two parts invested in business;**    
> And the fourth set aside    
> Against future misfortunes."

The [Dighajanu Sutta][7] states:

> "And what does it mean to maintain one's livelihood in tune? There is
> the case where a lay person, knowing the income and outflow of his
> wealth, maintains a livelihood in tune, neither a spendthrift nor a
> penny-pincher, [thinking], 'Thus will my income exceed my outflow, and
> my outflow will not exceed my income.'

The [Adiya Sutta][8] talks about the five types of benefits that can be obtained from wealth, which are summarized below:

> 'My wealth has been enjoyed,     
> my dependents supported,     
>     protected from calamities by me.     
> I have given supreme offerings    
>     & performed the five oblations.     
> I have provided for the virtuous,    
>     the restrained,    
>     followers of the holy life.    
>
> **For whatever aim a wise householder    
>     would desire wealth,    
>         that aim I have attained.**    
> I have done what will not lead to future distress.'    
> When this is recollected by a mortal,    
> a person established in the Dhamma of the Noble Ones,    
> he is praised in this life    
>     and, after death, rejoices in heaven.

Also from the [Anana Sutta][9] which talks about "the four kinds of bliss that can be attained in the proper season, on the proper occasions, by a householder partaking of sensuality", summarizes it as follows:

> Knowing the bliss of debtlessness,    
> & recollecting the bliss of having,    
> enjoying the bliss of wealth,    
> the mortal then sees clearly with discernment.    
> Seeing clearly — the wise one —     
> he knows both sides:    
> that these are not worth one sixteenth-sixteenth    
> of the bliss of blamelessness.

  [1]: http://www.accesstoinsight.org/ptf/dhamma/sila/pancasila.html
  [2]: http://www.accesstoinsight.org/ptf/dhamma/sila/index.html
  [3]: http://www.accesstoinsight.org/ptf/dhamma/sacca/sacca4/samma-ajivo/index.html
  [4]: https://buddhism.stackexchange.com/a/8518/471
  [5]: http://www.accesstoinsight.org/tipitaka/an/an05/an05.177.than.html
  [6]: http://www.accesstoinsight.org/tipitaka/dn/dn.31.0.ksw0.html
  [7]: http://www.accesstoinsight.org/tipitaka/an/an08/an08.054.than.html
  [8]: http://www.accesstoinsight.org/tipitaka/an/an05/an05.041.than.html
  [9]: http://www.accesstoinsight.org/tipitaka/an/an04/an04.062.than.html