What is integer overflow in R and how can it happen?

I have some calculation going on and get the following warning (i.e. not an error):

Warning messages:
1: In sum(myvar, na.rm = T) :
Integer overflow - use sum(as.numeric(.))

In this thread people state that integer overflows simply don't happen. Either R isn't overly modern or they are not right. However, what am I supposed to do here? If I use as.numeric as the warning suggests I might not account for the fact that information is lost way before. myvar is read form a .csv file, so shouldn't R figure out that some bigger field is needed? Does it already cut off something?

What's the max length of integer or numeric? Would you suggest any other field type / mode?

EDIT: I run:

R version 2.13.2 (2011-09-30) Platform: x86_64-apple-darwin9.8.0/x86_64 (64-bit) within R Studio