How to avoid pressing Enter with getchar() for reading a single character only?

This depends on your OS, if you are in a UNIX like environment the ICANON flag is enabled by default, so input is buffered until the next '\n' or EOF. By disabling the canonical mode you will get the characters immediately. This is also possible on other platforms, but there is no straight forward cross-platform solution.

EDIT: I see you specified that you use Ubuntu. I just posted something similar yesterday, but be aware that this will disable many default behaviors of your terminal.

#include<stdio.h>
#include <termios.h>            //termios, TCSANOW, ECHO, ICANON
#include <unistd.h>     //STDIN_FILENO


int main(void){   
    int c;   
    static struct termios oldt, newt;

    /*tcgetattr gets the parameters of the current terminal
    STDIN_FILENO will tell tcgetattr that it should write the settings
    of stdin to oldt*/
    tcgetattr( STDIN_FILENO, &oldt);
    /*now the settings will be copied*/
    newt = oldt;

    /*ICANON normally takes care that one line at a time will be processed
    that means it will return if it sees a "\n" or an EOF or an EOL*/
    newt.c_lflag &= ~(ICANON);          

    /*Those new settings will be set to STDIN
    TCSANOW tells tcsetattr to change attributes immediately. */
    tcsetattr( STDIN_FILENO, TCSANOW, &newt);

    /*This is your part:
    I choose 'e' to end input. Notice that EOF is also turned off
    in the non-canonical mode*/
    while((c=getchar())!= 'e')      
        putchar(c);                 

    /*restore the old settings*/
    tcsetattr( STDIN_FILENO, TCSANOW, &oldt);


    return 0;
}

You will notice, that every character appears twice. This is because the input is immediately echoed back to the terminal and then your program puts it back with putchar() too. If you want to disassociate the input from the output, you also have to turn of the ECHO flag. You can do this by simply changing the appropriate line to:

newt.c_lflag &= ~(ICANON | ECHO);