pull out p-values and r-squared from a linear regression

How do you pull out the p-value (for the significance of the coefficient of the single explanatory variable being non-zero) and R-squared value from a simple linear regression model? For example...

x = cumsum(c(0, runif(100, -1, +1)))
y = cumsum(c(0, runif(100, -1, +1)))
fit = lm(y ~ x)
summary(fit)

I know that summary(fit) displays the p-value and R-squared value, but I want to be able to stick these into other variables.

r-squared: You can return the r-squared value directly from the summary object summary(fit)$r.squared. See names(summary(fit)) for a list of all the items you can extract directly.

Model p-value: If you want to obtain the p-value of the overall regression model, this blog post outlines a function to return the p-value:

lmp <- function (modelobject) {
    if (class(modelobject) != "lm") stop("Not an object of class 'lm' ")
    f <- summary(modelobject)$fstatistic
    p <- pf(f[1],f[2],f[3],lower.tail=F)
    attributes(p) <- NULL
    return(p)
}

> lmp(fit)
[1] 1.622665e-05

In the case of a simple regression with one predictor, the model p-value and the p-value for the coefficient will be the same.

Coefficient p-values: If you have more than one predictor, then the above will return the model p-value, and the p-value for coefficients can be extracted using:

summary(fit)$coefficients[,4]  

Alternatively, you can grab the p-value of coefficients from the anova(fit) object in a similar fashion to the summary object above.

Notice that summary(fit) generates an object with all the information you need. The beta, se, t and p vectors are stored in it. Get the p-values by selecting the 4th column of the coefficients matrix (stored in the summary object):

summary(fit)$coefficients[,4] 
summary(fit)$r.squared

Try str(summary(fit)) to see all the info that this object contains.

Edit: I had misread Chase's answer which basically tells you how to get to what I give here.