Here's a selection of statistical functions that come with the standard R installation. You'll find many others in R packages.
Central Tendency and Variability
Function 
What it Calculates 
mean(x) 
Mean of the numbers in vector x. 
median(x) 
Median of the numbers in vector x 
var(x) 
Estimated variance of the population from which the numbers in vector x are sampled 
sd(x) 
Estimated standard deviation of the population from which the numbers in vector x are sampled 
scale(x) 
Standard scores (zscores) for the numbers in vector x 
Relative Standing
Function 
What it Calculates 
sort(x) 
The numbers in vector x in increasing order 
sort(x)[n] 
The nth smallest number in vector x 
rank(x) 
Ranks of the numbers (in increasing order) in vector x 
rank(x) 
Ranks of the numbers (in decreasing order) in vector x 
rank(x, ties.method= "average") 
Ranks of the numbers (in increasing order) in vector x, with tied numbers given the average of the ranks that the ties would have attained 
rank(x, ties.method= "min") 


Ranks of the numbers (in increasing order) in vector x, with tied numbers given the minimum of the ranks that the ties would have attained 
rank(x, ties.method = "max") 
Ranks of the numbers (in increasing order) in vector x, with tied numbers given the maximum of the ranks that the ties would have attained 

The 0^{th}, 25^{th}, 50^{th}, 75^{th}, and 100^{th} percentiles (i.e, the quartiles) of the numbers in vector x. (That's not a misprint: quantile(x) returns the quartiles of x.) 
ttests
Function 
What it Calculates 
t.test(x,mu=n, alternative = "two.sided") 
Twotailed ttest that the mean of the numbers in vector x is different from n. 
t.test(x,mu=n, alternative = "greater") 
Onetailed ttest that the mean of the numbers in vector x is greater than n. 
t.test(x,mu=n, alternative = "less") 
Onetailed ttest that the mean of the numbers in vector x is less than n. 
t.test(x,y,mu=0, var.equal = TRUE, alternative = "two.sided") 
Twotailed ttest that the mean of the numbers in vector x is different from the mean of the numbers in vector y. The variances in the two vectors are assumed to be equal. 
t.test(x,y,mu=0, alternative = "two.sided", paired = TRUE) 
Twotailed ttest that the mean of the numbers in vector x is different from the mean of the numbers in vector y. The vectors represent matched samples. 
Analysis of Variance (ANOVA)
Function 
What it Calculates 
aov(y~x, data = d) 
Singlefactor ANOVA, with the numbers in vector y as the dependent variable and the elements of vector x as the levels of the independent variable. The data are in data frame d. 
aov(y~x + Error(w/x), data = d) 
Repeated Measures ANOVA, with the numbers in vector y as the dependent variable and the elements in vector x as the levels of an independent variable. Error(w/x) indicates that each element in vector w experiences all the levels of x (i.e., x is a repeated measure). The data are in data frame d. 
aov(y~x*z, data = d) 
Twofactor ANOVA, with the numbers in vector y as the dependent variable and the elements of vectors x and z as the levels of the two independent variables. The data are in data frame d. 
aov(y~x*z + Error(w/z), data = d) 
Mixed ANOVA, with the numbers in vector z as the dependent variable and the elements of vectors x and y as the levels of the two independent variables. Error(w/z) indicates that each element in vector w experiences all the levels of z (i.e., z is a repeated measure). The data are in data frame d. 
Correlation and Regression
Function 
What it Calculates 
cor(x,y) 
Correlation coefficient between the numbers in vector x and the numbers in vector y 
cor.test(x,y) 
Correlation coefficient between the numbers in vector x and the numbers in vector y, along with a ttest of the significance of the correlation coefficient. 
lm(y~x, data = d) 
Linear regression analysis with the numbers in vector y as the dependent variable and the numbers in vector x as the independent variable. Data are in data frame d. 
coefficients(a) 
Slope and intercept of linear regression model a. 
confint(a) 
Confidence intervals of the slope and intercept of linear regression model a 
lm(y~x+z, data = d) 
Multiple regression analysis with the numbers in vector y as the dependent variable and the numbers in vectors x and z as the independent variables. Data are in data frame d. 
When you carry out an ANOVA or a regression analysis, store the analysis in a list. For example,
a < lm(y~x, data = d)
Then, to see the tabled results, use the summary() function:
summary(a)