Don't Appear Busy; Be Busy!
Many people who dispense dating advice will tell you to wait two hours before replying to a text, or two days before sending the first text after you’ve gotten someone’s number. The reason for this is to help give the impression that you’re someone who is busy, who has things going on, who will reply when they have a chance. Obviously, if every time you text someone they reply before you can close your phone, it might be a little strange; but this is not the same thing as honestly responding as soon as you see a message.
Don’t let someone tell you that you need to wait, staring at your phone and counting the minutes, so that you don’t seem ‘needy’. Here’s some better advice: if you find yourself grabbing your phone as soon as it buzzes, and you're rarely doing anything other than watching TV when it happens, perhaps you should try filling your life with more exciting and interesting things!
If it takes you an hour to reply to someone because you were at the gym, or flying a hang glider, or at a rock show, no reasonable person will hold it against you if you take a little longer to reply. If someone gets bent out of shape because of your honest response time, I would recommend you consider how they will react to this in the future. Some people prefer constant contact and instant communication, but I take a stand early on. I make it clear that I will never play games; I will reply when I have time or know the answer to the question they asked. If it takes me some time to reply, I am otherwise occupied; unless it's an emergency, they have to learn to be okay with it.
Granted, this is a bit of a balance; taking days to reply to someone will rarely be excused by being ‘busy,’ and replying within 30 seconds at any time of the day or night will likely be seen as clingy or boring. The idea is to be authentically busy, and courteous about how you respond to people.