How do I reference a regression model's coefficient's standard errors?             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  10.2758     0.5185  19.817  < 2e-16 ***
rprice2      -1.8581     0.5139  -3.616 0.000696 ***

I would like to use the Std. Error of rprice2 to make other calculations. I know to reference any of the objects in the model, I use the syntax model$object, but what is the syntax for referencing the std errors?
 A: To extract without performing any other calculations, while using the object$model syntax:
summary(model)$coefficients["rprice2","Std. Error"]

A: As I understand it you want to do this in R:
f <- lm(speed~dist, data=cars)
coef(f)
confint(f)
sd = sqrt(diag(vcov(f)))
cbind("2.5 %"=-sd*1.96+coef(f),"97.5 %"=sd*1.96+coef(f))

Gives:
> coef(f)
(Intercept)        dist 
  8.2839056   0.1655676 
> confint(f)
                2.5 %     97.5 %
(Intercept) 6.5258378 10.0419735
dist        0.1303926  0.2007426
> cbind("2.5 %"=-sd*1.96+coef(f),"97.5 %"=sd*1.96+coef(f))
                2.5 %    97.5 %
(Intercept) 6.5701120 9.9976992
dist        0.1312784 0.1998568

A: To obtain a matrix with the results of the linear regression:
> coef(summary(f))

To extract a specific value from the matrix:
> coef(summary(f))["rprice2","Std. Error"]
[1] 0.5139 

A: Quite generally you want the vcov function which provides the complete parameter covariance matrix.  To get the regular asymptotic standard errors reported by summary you can use
se <- sqrt(diag(vcov(model)))

btw you would want the off-diagonals of vcov(model) to get marginal effects for interaction terms: see Brambor et al. (2006).
Note also packages like sandwich devoted to constructing different types of standard errors, e.g. ones 'robust' to various types of violations.
