How can I find if a particular package exists on my Android device?

Call any of the below method with the package name.

import android.content.pm.PackageManager;

// ...

    public boolean isPackageExisted(String targetPackage){
        List<ApplicationInfo> packages;
        PackageManager pm;

        pm = getPackageManager();        
        packages = pm.getInstalledApplications(0);
        for (ApplicationInfo packageInfo : packages) {
            if(packageInfo.packageName.equals(targetPackage))
                return true;
        }
        return false;
    }

---

 import android.content.pm.PackageManager;

 public boolean isPackageExisted(String targetPackage){
   PackageManager pm=getPackageManager();
   try {
     PackageInfo info=pm.getPackageInfo(targetPackage,PackageManager.GET_META_DATA);
   } catch (PackageManager.NameNotFoundException e) {
     return false;
   }  
   return true;
 }

Without using a try-catch block or iterating through a bunch of packages:

public static boolean isPackageInstalled(Context context, String packageName) {
    final PackageManager packageManager = context.getPackageManager();
    Intent intent = packageManager.getLaunchIntentForPackage(packageName);
    if (intent == null) {
        return false;
    }
    List<ResolveInfo> list = packageManager.queryIntentActivities(intent, PackageManager.MATCH_DEFAULT_ONLY);
    return list.size() > 0;
}