Easy way to export multiple data.frame to multiple Excel worksheets

There's a new library in town, from rOpenSci: writexl

Portable, light-weight data frame to xlsx exporter based on libxlsxwriter. No Java or Excel required

I found it better and faster than the above suggestions (working with the dev version):

library(writexl)
sheets <- list("sheet1Name" = sheet1, "sheet2Name" = sheet2) #assume sheet1 and sheet2 are data frames
write_xlsx(sheets, "path/to/location")

You can also use the openxlsx library to export multiple datasets to multiple sheets in a single workbook.The advantage of openxlsx over xlsx is that openxlsx removes the dependencies on java libraries.

Write a list of data.frames to individual worksheets using list names as worksheet names.

require(openxlsx)
list_of_datasets <- list("Name of DataSheet1" = dataframe1, "Name of Datasheet2" = dataframe2)
write.xlsx(list_of_datasets, file = "writeXLSX2.xlsx")

You can write to multiple sheets with the xlsx package. You just need to use a different sheetName for each data frame and you need to add append=TRUE:

library(xlsx)
write.xlsx(dataframe1, file="filename.xlsx", sheetName="sheet1", row.names=FALSE)
write.xlsx(dataframe2, file="filename.xlsx", sheetName="sheet2", append=TRUE, row.names=FALSE)

Another option, one that gives you more control over formatting and where the data frame is placed, is to do everything within R/xlsx code and then save the workbook at the end. For example:

wb = createWorkbook()

sheet = createSheet(wb, "Sheet 1")

addDataFrame(dataframe1, sheet=sheet, startColumn=1, row.names=FALSE)
addDataFrame(dataframe2, sheet=sheet, startColumn=10, row.names=FALSE)

sheet = createSheet(wb, "Sheet 2")

addDataFrame(dataframe3, sheet=sheet, startColumn=1, row.names=FALSE)

saveWorkbook(wb, "My_File.xlsx")

In case you might find it useful, here are some interesting helper functions that make it easier to add formatting, metadata, and other features to spreadsheets using xlsx: http://www.sthda.com/english/wiki/r2excel-read-write-and-format-easily-excel-files-using-r-software

Many good answers here, but some of them are a little dated. If you want to add further worksheets to a single file then this is the approach I find works for me. For clarity, here is the workflow for openxlsx version 4.0

# Create a blank workbook
OUT <- createWorkbook()

# Add some sheets to the workbook
addWorksheet(OUT, "Sheet 1 Name")
addWorksheet(OUT, "Sheet 2 Name")

# Write the data to the sheets
writeData(OUT, sheet = "Sheet 1 Name", x = dataframe1)
writeData(OUT, sheet = "Sheet 2 Name", x = dataframe2)

# Export the file
saveWorkbook(OUT, "My output file.xlsx")

EDIT

I've now trialled a few other answers, and I actually really like @Syed's. It doesn't exploit all the functionality of openxlsx but if you want a quick-and-easy export method then that's probably the most straightforward.