Show correlations as an ordered list, not as a large matrix

Building off of @Marek's answer. Eliminates diagonal and duplicates

data = as.data.frame( as.table( z ) )
combinations = combn( colnames( z ) , 2 , FUN = function( x ) { paste( x , collapse = "_" ) } )
data = data[ data$Var1 != data$Var2 , ]
data = data[ paste( data$Var1 , data$Var2 , sep = "_" ) %in% combinations , ]

I always use

zdf <- as.data.frame(as.table(z))
zdf
#    Var1 Var2     Freq
# 1     a    a  1.00000
# 2     b    a -0.99669
# 3     c    a -0.14063
# 4     d    a -0.28061
# 5     e    a  0.80519

Then use subset(zdf, abs(Freq) > 0.5) to select significant values.

library(reshape)

z[z == 1] <- NA #drop perfect
z[abs(z) < 0.5] <- NA # drop less than abs(0.5)
z <- na.omit(melt(z)) # melt! 
z[order(-abs(z$value)),] # sort