How to check an Android device is HDPI screen or MDPI screen?

As of 2018, you can use the below method -

    public static String getDeviceDensityString(Context context) {
    switch (context.getResources().getDisplayMetrics().densityDpi) {
        case DisplayMetrics.DENSITY_LOW:
            return "ldpi";
        case DisplayMetrics.DENSITY_MEDIUM:
            return "mdpi";
        case DisplayMetrics.DENSITY_TV:
        case DisplayMetrics.DENSITY_HIGH:
            return "hdpi";
        case DisplayMetrics.DENSITY_260:
        case DisplayMetrics.DENSITY_280:
        case DisplayMetrics.DENSITY_300:
        case DisplayMetrics.DENSITY_XHIGH:
            return "xhdpi";
        case DisplayMetrics.DENSITY_340:
        case DisplayMetrics.DENSITY_360:
        case DisplayMetrics.DENSITY_400:
        case DisplayMetrics.DENSITY_420:
        case DisplayMetrics.DENSITY_440:
        case DisplayMetrics.DENSITY_XXHIGH:
            return "xxhdpi";
        case DisplayMetrics.DENSITY_560:
        case DisplayMetrics.DENSITY_XXXHIGH:
            return "xxxhdpi";
    }
}

But as @Ted pointed always consult the official docs before using

density = getResources().getDisplayMetrics().density;

// return 0.75 if it's LDPI
// return 1.0 if it's MDPI
// return 1.5 if it's HDPI
// return 2.0 if it's XHDPI
// return 3.0 if it's XXHDPI
// return 4.0 if it's XXXHDPI

You can check the screen density with:

switch (getResources().getDisplayMetrics().densityDpi) {
case DisplayMetrics.DENSITY_LOW:
    // ...
    break;
case DisplayMetrics.DENSITY_MEDIUM:
    // ...
    break;
case DisplayMetrics.DENSITY_HIGH:
    // ...
    break;
case DisplayMetrics.DENSITY_XHIGH:
    // ...
    break;
}

EDIT Be aware that as Android evolves, other values should be included in the switch cases. As of this edit, this includes DisplayMetrics.DENSITY_TV and DisplayMetrics.DENSITY_XXHIGH. Consult the docs for the latest info; I'm not going to bother maintaining this answer.