Like your .bashrc, .vimrc, or many other dotfiles you may have in your home directory, your .Rprofile is sourced every time you start an R session. On Mac and Linux, this file is usually located in ~/.Rprofile. On Windows it's buried somewhere in the R program files. Over the years I've grown and pruned my .Rprofile to set various options and define various "utility" functions I use frequently at the interactive prompt.
One of the dangers of defining too many functions in your .Rprofile is that your code becomes less portable, and less reproducible. For example, if I were to define adf() as a shortcut to as.data.frame(), code that I send to other folks using adf() would return errors that the adf object doesn't exist. This is a risk that I'm fully aware of in regards to setting the option stringsAsFactors=FALSE, but it's a tradeoff I'm willing to accept for convenience. Most of the functions I define here are useful for exploring interactively. In particular, the n() function below is handy for getting a numbered list of all the columns in a data frame; lsp() and lsa() list all functions in a package, and list all objects and classes in the environment, respectively (and were taken from Karthik Ram's .Rprofile); and the o() function opens the current working directory in a new Finder window on my Mac. In addition to a few other functions that are self-explanatory, I also turn off those significance stars, set a default CRAN mirror so it doesn't ask me all the time, and source in the biocLite() function for installing Bioconductor packages (note: this makes R require web access, which might slow down your R initialization).
Finally, you'll notice that I'm creating a new hidden environment, and defining all the functions here as objects in this hidden environment. This allows me to keep my workspace clean, and remove all objects from that workspace without nuking any of these utility functions.
I used to keep my .Rprofile synced across multiple installations using Dropbox, but now I keep all my dotfiles in a single git-versioned directory, symlinked where they need to go (usually ~/). My .Rprofile is below: feel free to steal or adapt however you'd like.