For bulk sequencing of human exmaples, If the clean reads number is larger than 50M, I think two repeats are enough. In fact, you will found the correlation between two bilogical repeats would be very good. 

But if it is the single cell sequencing, the number is decided on your question!

Are you going to do gene expression analysis, or something else?

I would recommend doing a minimum of 2 biological replicates per sample. So that would be 6 RNAseq libraries total, two for each of your three tissue types. Three biological replicates would be even better if that's possible.

Although it depends on the type of machine and kit used, in general you will get a few hundred million read pairs per lane on a HiSeq, so multiplexing these libraries on two lanes would likely give you enough coverage (ie >50M reads/library).

Hello! You can do a pilot experiment to estimate the number of samples and sequencing depth necessary to get you statistically significant data. Try apriori power analysis using Scotty, http://scotty.genetics.utah.edu/ One of the problems with cancer (and many tissues) is a heterogeneous mixture of cell types and gene expression. For example, if you are interested in one cells gene expression and you have a mixture of 200 cell types and some types also express the gene of interest the effect size is diluted by the average of that genes expression across the mixture and perhaps even masked if the contaminating cells express the gene of interest at very high levels. On the other hand sometimes the background gene expression is helpful to make uniquely affected genes stand out as they are not expressed, or have very low expression in the background. From our perspective the worst thing is to get poor/useless data. I would scale way back and just try the pilot on one of the three conditions and then using the Scotty info just well sequence the one pair and process completely making sure that I am getting the data I need, before proceeding with the other cell types. I use htseq-count and edgeR for statistical analysis, and for these software three samples is best. Good luck!!

Because these are patient samples and you're dealing with cancer the biological variability is going to be very large and will require a lot of statistical power to pick up anything significant. You're unlikely to be able to publish in a decent journal without tens to hundreds of patient samples. For example, this one published earlier this year had 275 patients

http://breast-cancer-research.biomedcentral.com/articles/10.1186/s13058-016-0710-8

The above responses have good advice. The numbers I threw out were sort of a general guide-line coming from someone working with non-mammalian systems. I should have said that your sampling will also depend on the question you're asking and might require many biological replicates form different "patient samples" in order to get statistical power. For differential expression analysis I use htseq and DEseq. Looking for overlap between DEseq and edgeR results can provide an additional layer of filtering for true differentially expressed genes.

For Differential Gene expression, I would say bare minimum 3 biological replicates. And 3 is at the lowest combination of your experimental factors.

For ex: Total 6 samples when you have two conditions:

treated1,treated2,treated3,control1,control2,control3

And if you have say 2 families as well, then 6x2=12 samples total.

fam1

treated1,treated2,treated3,control1,control2,control3

fam2

treated1,treated2,treated3,control1,control2,control3

assuming you will control for family later ~family+condition.

But, in practice it might be better to sequence one or two more samples than you actually need, because you don't know for sure, if all 3 would actually work and produce usable results. 

Attached study suggests minimum 6 replicates for detecting medium to high fold change Diff Exp Genes. And min 12 replicates if you are interested in low fold change genes as well.

http://rnajournal.cshlp.org/content/22/6/839.short