A quick guide to choice of sample sizes for Cohen's effect sizes
Dunlap and Myers (1997) suggest rules of thumb for sample sizes using Cohen's effect size rules of thumb and equations that they have derived in some simple cases. These are given in the table. The sample sizes guarantee between 80% and 90% power to detect the given effect sizes.
Effect Size 
Formula 
Small 
Medium 
Large 

Cohen's d unpaired t, 
$$\frac{\mbox{16}}{\mbox{d}^text{2}}$$ + 2 
0.2 
0.5 
0.8 

equal group sizes 

402 
66 
28 

Correlation 
8/$$r^text{2}$$ 
0.1 
0.3 
0.5 

Total sample size 

800 
88 
32 

$$\phi$$, 2x2 table 
8/$$\phi^text{2}$$ 
0.1 
0.3 
0.5 

Total sample size 

800 
88 
32 
Dunlap and Myers (1997) show in their appendix that for a 2x2 table of proportions of form

Column 1 
Column 2 
Row 1 
$$p_text{11}$$ 
$$p_text{12}$$ 
Row 2 
$$p_text{21}$$ 
$$p_text{22}$$ 
with
A = $$\frac{p_text{11}}{p_text{11}+p_text{12}}$$, B = $$\frac{p_text{21}}{p_text{21}+p_text{22}}$$
C = $$\frac{p_text{11}}{p_text{11}+p_text{21}}$$, D = $$\frac{p_text{12}}{p_text{12}+p_text{22}}$$
then we can define $$\phi = \sqrt{\mbox{abs(AB)} \mbox{abs(CD)}}$$
In addition Maxwell (2000) mentions rules of thumb for power to detect the $$R^text{2}$$ of a single predictor with outcome in a multiple regression with a total of p predictors and a type I error of 0.05. These are give below:
Regression on p predictors 
Small:$$R^text{2}$$=0.02 
Medium:$$R^text{2}$$=0.13 
Large:$$R^text{2}$$=0.26 

Total sample size 
80% Power 
392+p 
52+p 
22+p 

Total sample size 
90% Power 
526+p 
70+p 
30+p 
Reference
Dunlap WP, Myers L. (1997) Approximating power for significance tests with one degree of freedom. Psychological methods 2(2) 186191.
Maxwell SE (2000) Sample size and multiple regression analysis, Psychological methods 5(4) 434458.