Import an RDATA, SPSS, SAS, or STATA file into Mathematica

You are right - those formats are for statistical software packages.
I've noticed in Big Data discussions that Mathematica does not want to extend the range of acceptable data formats leaving the job to third-party software. I would recommend to use software like 'Stat/Transfer', which is a usual practice for such tasks. If you take data from WVS, say Stata's .dta which I prefer, you may easily transfer it to .CSV or .DAT file.
Just take an option ASCII - Delimited as shown below.
Then .csv is imported to Mathematica as usual.
Another option is to use ASCII Fixed Format + All Programs which will produce .dat file also easily imported to Mathematica (I've checked both cases).

This should do the trick - disclaimer the file is 1.4Gb so everything takes a veerryyy long time on my MacBook air, and you will need an active internet connection for InstallR to work. Note you have to escape internal R file paths and anything else that uses a double quote.

Firstly download the rdata version of the file from the link given.

Needs["RLink`"];

InstallR[];

REvaluate[
"load("~/Downloads/WVS_Longitudinal_1981_2014_R_v2015_04_18.rdata")"];

(*{".Traceback","WVS_Longitudinal_1981_2014_R_v2015_04_18"}*)

Writes the data into an R Dataset called WVS_Longitudinal_1981_2014_R_v2015_04_18

REvaluate["write.csv(WVS_Longitudinal_1981_2014_R_v2015_04_18,file=
"WVS_data_rlink.csv")"];

Writes the data back out to a CSV. Note in this case the file is a simple tabular one. This might be more problematic for some of the more complex data structures that .rdata format permits.

Theoreticall you can actually import the WVS_Longitudinal_1981_2014_R_v2015_04_18 data directly into MMA and work with it natively from that point but requires me working through the rLink tutorial a bit more than I have time for right now. :)

EDIT : Some useful tips to explore the data directly.

Get Column Names

REvaluate["names(WVS_Longitudinal_1981_2014_R_v2015_04_18)"] // Short

Get a single column in this case S001

REvaluate["WVS_Longitudinal_1981_2014_R_v2015_04_18$S001"]

Get the first 10 lines of the R data.frame note the R data objects in there. head is like the unix head not Head[] This data is so wide and deep its hard to get it in a readable format without subsetting and slicing and dicing.

REvaluate["head(WVS_Longitudinal_1981_2014_R_v2015_04_18,n=10)"]

With the ability to connect to Python I found this snippet of code helpful. It imports a STATA .dta file using pandas and then outputs it as a Wolfram Dataset.

     importDTAMP[fileName_] := Module[{}, 
 python37 = 
       StartExternalSession[<|"System" -> "Python", "Version" -> "3.7.3"|>];
      pythonFileName = StringReplace[fileName, "" -> "/"];
      
      ds = ExternalEvaluate[
        python37,
        "
         import pandas as pd;
         path = '" <> pythonFileName <> "';
         df = pd.read_stata(path);
         df
         "
        ];
      
      DeleteObject[python37];
      ds
      
      ]