read word by word from file in C++

First of all, don't loop while (!eof()), it will not work as you expect it to because the eofbit will not be set until after a failed read due to end of file.

Secondly, the normal input operator >> separates on whitespace and so can be used to read "words":

std::string word;
while (file >> word)
{
    ...
}

I have edited the function for you,

void readFile()
{
    ifstream file;
    file.open ("program.txt");
    if (!file.is_open()) return;

    string word;
    while (file >> word)
    {
        cout<< word << '\n';
    }
}

what you are doing here is reading one character at a time from the input stream and assume that all the characters between " " represent a word. BUT it's unlikely to be a " " after the last word, so that's probably why it does not work:

"word1 word2 word2EOF"

As others have said, you are likely reading past the end of the file as you're only checking for x != ' '. Instead you also have to check for EOF in the inner loop (but in this case don't use a char, but a sufficiently large type):

while ( ! file.eof() )
{
    std::ifstream::int_type x = file.get();

    while ( x != ' ' && x != std::ifstream::traits_type::eof() )
    {
        word += static_cast<char>(x);
        x = file.get();
    }
    std::cout << word << '\n';
    word.clear();
}

But then again, you can just employ the stream's streaming operators, which already separate at whitespace (and better account for multiple spaces and other kinds of whitepsace):

void readFile(  )
{
    std::ifstream file("program.txt");
    for(std::string word; file >> word; )
        std::cout << word << '\n';
}

And even further, you can employ a standard algorithm to get rid of the manual loop altogether:

#include <algorithm>
#include <iterator>

void readFile(  )
{
    std::ifstream file("program.txt");
    std::copy(std::istream_iterator<std::string>(file), 
              std::istream_itetator<std::string>(), 
              std::ostream_iterator<std::string>(std::cout, "\n"));
}

text file :

code :

#include <fstream>
#include <iostream>
#include <string>


using namespace std;
int main()
{

ifstream file("DB_name_age.txt");
int index;
string name;
int age;

if(file.is_open()) 
{
    while(file  >>index >> name >>age)  
    {
        cout << index <<" "<<name <<" "<<age << endl;
    }


   }else{
    cout<< "file open fail" <<endl;
  }
  return 0;
 }

visual explanation: