Well, if sample were free, the optimal amount would be a census. Of course sample isn't free of cost or effort, so we have to trade off the benefit of more sample with the cost.
There are a couple of ways to think about this - there are calculations and there are rules of thumb. The latter are distilled from experience and often provide valuable guidance for practitioners. If you are publishing in support of a government grant, however, the sample size considerations are usually more stringent and you may want to use a formula.
The rule of thumb we often recommend at Sawtooth Software is to use the Design Test feature of our software to run random respondents through your design and to choose a sample size that gives you standard errors no larger than 0.05 for main effects and 0.10 for interactions. Of course you don't need our software to do this as you can run artificial data through any multinomial logit estimation software to get the standard errors.
A formula (and an R program to bring it to life) is available in an article you can find here: http://www.ncbi.nlm.nih.gov/pubmed/25726010.