Table of sample sizes required for tests of nonzero Kendall, Spearman and Pearson correlations
We assume 90% power and a Type I error of 5%
Null hypothesis : correlation = 0;
Alternative: correlation = nonzero value
If you know the sign of the nonzero correlation the test is onetailed otherwise it is twotailed.
Computations using methods in Kraemer, HC & Thiemann, S (1987) How Many Subjects? Statistical Power Analysis in Research. Sage:London.
Power calculator also available for the Pearson correlation.
 Dunlap WP and Myers L (1997) show that for a Pearson correlation, r, 8/$$r^text{2}$$ gives a total sample size with at least 80% power.
Correlations of 0.1, 0.3 and 0.5 correspond to small, medium and high correlations using rules of thumb.

1tail 
2tail 

correlation 
Kendall 
Spearman 
Pearson 
Kendall 
Spearman 
Pearson 

0.1 
1041 
1013 
854 
1277 
1111 
1047 

0.2 
224 
250 
212 
274 
307 
259 

0.3 
106 
107 
93 
129 
130 
113 

0.4 
58 
62 
51 
70 
75 
62 

0.5 
37 
39 
32 
44 
46 
38 

0.6 
25 
26 
21 
29 
30 
25 

0.7 
18 
19 
15 
21 
21 
17 

0.8 
13 
<14 
<10 
15 
15 
12 

0.9 
9 
<10 
<10 
11 
11 
<10 
Reference
Dunlap WP and Myers L (1997) Approximating Power for significance tests with one degree of freedom. Psychological Methods 2(2) 186191.