std::boolalpha and std::noboolalpha - switch between textual and numeric representation of booleans.

std::cout << std::boolalpha << 1;
// Output: true

std::cout << std::noboolalpha << false;
// Output: 0

bool boolValue;
std::cin >> std::boolalpha >> boolValue;
std::cout << "Value \\"" << std::boolalpha << boolValue
          << "\\" was parsed as " << std::noboolalpha << boolValue;
// Input: true
// Output: Value "true" was parsed as 0

std::showbase and std::noshowbase - control whether prefix indicating numeric base is used.

std::dec (decimal), std::hex (hexadecimal) and std::oct (octal) - are used for changing base for integers.

#include <sstream>

std::cout << std::dec << 29 << ' - '
          << std::hex << 29 << ' - '
          << std::showbase << std::oct << 29 << ' - '
          << std::noshowbase << 29  '\\n';
int number;
std::istringstream("3B") >> std::hex >> number;
std::cout << std::dec << 10;
// Output: 22 - 1D - 35 - 035
// 59

Default values are std::ios_base::noshowbase and std::ios_base::dec.

If you want to see more about std::istringstream check out the <sstream> header.

std::uppercase and std::nouppercase - control whether uppercase characters are used in floating-point and hexadecimal integer output. Have no effect on input streams.

std::cout << std::hex << std::showbase
              << "0x2a with nouppercase: " << std::nouppercase << 0x2a << '\\n'
              << "1e-10 with uppercase: " << std::uppercase << 1e-10 << '\\n'
}
// Output: 0x2a with nouppercase: 0x2a
// 1e-10 with uppercase: 1E-10

Default is std::nouppercase.

std::setw(n) - changes the width of the next input/output field to exactly n.

The width property n is resetting to 0 when some functions are called (full list is here).

std::cout << "no setw:" << 51 << '\\n'
          << "setw(7): " << std::setw(7) << 51 << '\\n'
          << "setw(7), more output: " << 13
          << std::setw(7) << std::setfill('*') << 67 << ' ' << 94 << '\\n';

char* input = "Hello, world!";
char arr[10];
std::cin >> std::setw(6) >> arr;
std::cout << "Input from \\"Hello, world!\\" with setw(6) gave \\"" << arr << "\\"\\n";

// Output: 51
// setw(7):      51
// setw(7), more output: 13*****67 94

// Input: Hello, world!
// Output: Input from "Hello, world!" with setw(6) gave "Hello"

Default is std::setw(0).

std::left, std::right and std::internal - modify the default position of the fill characters by setting std::ios_base::adjustfield to std::ios_base::left, std::ios_base::right and std::ios_base::internal correspondingly. std::left and std::right apply to any output, std::internal - for integer, floating-point and monetary output. Have no effect on input streams.

#include <locale>
...

std::cout.imbue(std::locale("en_US.utf8"));

std::cout << std::left << std::showbase << std::setfill('*')
          << "flt: " << std::setw(15) << -9.87  << '\\n'
          << "hex: " << std::setw(15) << 41 << '\\n'
          << "  $: " << std::setw(15) << std::put_money(367, false) << '\\n'
          << "usd: " << std::setw(15) << std::put_money(367, true) << '\\n'
          << "usd: " << std::setw(15)
          << std::setfill(' ') << std::put_money(367, false) << '\\n';
// Output:
// flt: -9.87**********
// hex: 41*************
//   $: $3.67**********
// usd: USD *3.67******
// usd: $3.67          

std::cout << std::internal << std::showbase << std::setfill('*')
          << "flt: " << std::setw(15) << -9.87  << '\\n'
          << "hex: " << std::setw(15) << 41 << '\\n'
          << "  $: " << std::setw(15) << std::put_money(367, false) << '\\n'
          << "usd: " << std::setw(15) << std::put_money(367, true) << '\\n'
          << "usd: " << std::setw(15)
          << std::setfill(' ') << std::put_money(367, true) << '\\n';
// Output:
// flt: -**********9.87
// hex: *************41
//   $: $3.67**********
// usd: USD *******3.67
// usd: USD        3.67

std::cout << std::right << std::showbase << std::setfill('*')
          << "flt: " << std::setw(15) << -9.87  << '\\n'
          << "hex: " << std::setw(15) << 41 << '\\n'
          << "  $: " << std::setw(15) << std::put_money(367, false) << '\\n'
          << "usd: " << std::setw(15) << std::put_money(367, true) << '\\n'
          << "usd: " << std::setw(15)
          << std::setfill(' ') << std::put_money(367, true) << '\\n';
// Output:
// flt: **********-9.87
// hex: *************41
//   $: **********$3.67
// usd: ******USD *3.67
// usd:       USD  3.67

Default is std::left.

std::fixed, std::scientific, std::hexfloat [C++11] and std::defaultfloat [C++11] - change formatting for floating-point input/output.

std::fixed sets the std::ios_base::floatfield to std::ios_base::fixed,