In my case, the configuration file name was different. So, running the command specifying the conf file solved my issue.
>> karma start unit-tests.conf.js
No captured browser, open http://localhost:9876/
...
And for 'PhantomJS', opening the link specified(localhost:9876) in the browser executes the test cases.
Hope it helps. :)
EDIT 1: My Karma Config File
module.exports = function(config) {
  config.set({
    // base path that will be used to resolve all patterns (eg. files, exclude)
    basePath: '',
    // frameworks to use
    // available frameworks: https://npmjs.org/browse/keyword/karma-adapter
    frameworks: ['jasmine'],
    // list of files / patterns to load in the browser
    files: [
      './node_modules/angular/angular.js',
      './node_modules/angular-ui-router/release/angular-ui-router.js',
      './node_modules/angular-mocks/angular-mocks.js',
      './app/services/users/users.js',
      './app/app.js',
      './app/services/users/users.spec.js'
    ],
    // list of files to exclude
    exclude: [
    ],
    // preprocess matching files before serving them to the browser
    // available preprocessors: https://npmjs.org/browse/keyword/karma-preprocessor
    preprocessors: {
    },
    // test results reporter to use
    // possible values: 'dots', 'progress'
    // available reporters: https://npmjs.org/browse/keyword/karma-reporter
    reporters: ['spec'],
    // web server port
    port: 9876,
    // enable / disable colors in the output (reporters and logs)
    colors: true,
    // level of logging
    // possible values: config.LOG_DISABLE || config.LOG_ERROR || config.LOG_WARN || config.LOG_INFO || config.LOG_DEBUG
    logLevel: config.LOG_INFO,
    // enable / disable watching file and executing tests whenever any file changes
    autoWatch: true,
    // start these browsers
    // available browser launchers: https://npmjs.org/browse/keyword/karma-launcher
    browsers: ['Chrome'],
    // Continuous Integration mode
    // if true, Karma captures browsers, runs the tests and exits
    singleRun: false,
    // Concurrency level
    // how many browser should be started simultaneous
    concurrency: Infinity
  })
}