I only have access to free GIS softwares as DIVA-GIS and all the solutions I have read can only be applied to ArcGIS or other license software. Any advice?
You can try using R software (https://r-project.org), there package which allow you to read and write tif image (http://cran.r-project.org/web/packages/rtiff/rtiff.pdf), than you can save this image into different format lika ASCII, xlsx or CSV (http://www.statmethods.net/input/exportingdata.html)
In your R code, your are talking about .grd files but I do want to convert .tif files. Secondly can you say to me what is the function system.file? Does it refer to the file path or is it for something else?
Paulo suggested the approach I would use. I would add that you might need to have the "rgdal" library as well as the "raster" library installed in your R system and you might stumble across a slightly different sequence of commands. GDAL reads and writes nearly everything, and having it at my fingertips in an R session (via rdgal) is wonderful. Also, I don't think you need to have the standalone version of GDAL on your machine to use rgdal, but I could be wrong about that.
Also, I didn't see anyone mention GRASS. That used to be (and may still be) a quite powerful GIS, including the capability to read and write many file formats (probably via GDAL).
You should try to provide a minimal reproducible example of your data, or access to it, and the code or the procedure you're using and the error your are getting.
You can easily access Wordclim variables from R raster package. Try getData('worldclim', var='choosen_var', res=res, lon=lon, lat=lat). Replacing var, res, lat, lon.
In ArcMap go to Arctoolbox > Conversion tools > Raster. Input your raster file. Then in the output file directory, make sure you put the extension .asc to your file name. Instead of just putting for instance "outputfilename", put "outputfilename.asc".
You could try to use R-software (http://www.r-project.org/). Absolutely free and powerful software to work with raster image (read, manipulation, plot) using raster package (http://cran.r-project.org/web/packages/raster/index.html).
In ArcMap go to Arctoolbox > Conversion tools > From Raster to ASCII. It is essential that in the output file directory you put the extension ".asc" in the name of your file. Example: "outputfile.asc".
@Marek Kowalewski can the gdal_translate be used with GeoTiff raster with multiple bands to an .ASC file. I am getting the Warning 6:XYZ driver only uses the first band of the dataset. Can you suggest a way to overcome this. Thanks