Extract random effect variances from lme4 mer model object

This answer is heavily based on that on @Ben Bolker's, but if people are new to this and want the values themselves, instead of just a printout of the values (as OP seems to have wanted), then you can extract the values as follows:

Convert the VarCorr object to a data frame.

re_dat = as.data.frame(VarCorr(study))

Then access each individual value:

int_vcov = re_dat[1,'vcov']
resid_vcov = re_dat[2,'vcov']

With this method (specifying rows and columns in the date frame you created) you can access whichever values you'd like.

lmer returns an S4 object, so this should work:

remat <- summary(study)@REmat
print(remat, quote=FALSE)

Which prints:

 Groups   Name        Variance Std.Dev.
 Subject  (Intercept) 1378.18  37.124  
 Residual              960.46  30.991  

...In general, you can look at the source of the print and summary methods for "mer" objects:

class(study) # mer
selectMethod("print", "mer")
selectMethod("summary", "mer")

> attributes(summary(study))$REmat
 Groups     Name          Variance  Std.Dev.
 "Subject"  "(Intercept)" "1378.18" "37.124"
 "Residual" ""            " 960.46" "30.991"

Some of the other answers are workable, but I claim that the best answer is to use the accessor method that is designed for this -- VarCorr (this is the same as in lme4's predecessor, the nlme package).

UPDATE in recent versions of lme4 (version 1.1-7, but everything below is probably applicable to versions >= 1.0), VarCorr is more flexible than before, and should do everything you want without ever resorting to fishing around inside the fitted model object.

library(lme4)
study <- lmer(Reaction ~ Days + (1|Subject), data = sleepstudy)
VarCorr(study)
##  Groups   Name        Std.Dev.
##  Subject  (Intercept) 37.124  
##  Residual             30.991

By default VarCorr() prints standard deviations, but you can get variances instead if you prefer:

print(VarCorr(study),comp="Variance")
##  Groups   Name        Variance
##  Subject  (Intercept) 1378.18 
##  Residual              960.46 

(comp=c("Variance","Std.Dev.") will print both).

For more flexibility, you can use the as.data.frame method to convert the VarCorr object, which gives the grouping variable, effect variable(s), and the variance/covariance or standard deviation/correlations:

as.data.frame(VarCorr(study))
##        grp        var1 var2      vcov    sdcor
## 1  Subject (Intercept) <NA> 1378.1785 37.12383
## 2 Residual        <NA> <NA>  960.4566 30.99123

Finally, the raw form of the VarCorr object (which you probably shouldn't mess with you if you don't have to) is a list of variance-covariance matrices with additional (redundant) information encoding the standard deviations and correlations, as well as attributes ("sc") giving the residual standard deviation and specifying whether the model has an estimated scale parameter ("useSc").

unclass(VarCorr(fm1))
## $Subject
##             (Intercept)      Days
## (Intercept)  612.089748  9.604335
## Days           9.604335 35.071662
## attr(,"stddev")
## (Intercept)        Days 
##   24.740448    5.922133 
## attr(,"correlation")
##             (Intercept)       Days
## (Intercept)  1.00000000 0.06555134
## Days         0.06555134 1.00000000
## 
## attr(,"sc")
## [1] 25.59182
## attr(,"useSc")
## [1] TRUE
##