Why can't I catch Pokemon in Pokemon Go anymore?

You are probably soft banned.

Soft banning occurs when the game detects that you're moving around too quickly. This can happen if:

• You use GPS spoofing to fake your current location.
• You travel in a vehicle at an excessive speed.
• You disable your GPS, travel a significant distance, then re-enable it.
• You lose data service, travel a significant distance, then re-connect.

The following are symptoms of a soft ban:

• When you throw a Pokeball at a Pokemon, it wiggles around a bit, then flees without fail.
• When you try and spin a Pokestop, it never turns purple, and you never get any items.
• You are unable to challenge or train at any gyms.

If you are soft banned, the ban will lift itself within a few hours.

Here's a video of what a soft ban looks like:

Currently, there is speculation that the soft ban mechanism functions similarly to the "bubble effect" in Ingress, the last ARG developed by Niantic. This effect is explained here:

No matter what speed you are traveling, you can perform an action as long as you haven't performed one in the last 15 minutes. Once you perform an action, a figurative "bubble" is created. This bubble expands at the rate of 60 km/h. If you travel out of this bubble, you will not be able to successfully perform actions. So, once you slow down, you have to wait for the bubble to catch up with you before you can perform actions again. After 15 minutes, the bubble goes away, and you can perform actions again even if the bubble hadn't caught up to you yet.

(For US readers, 60 km/h is approximately 37 mph.)

It's quite possible that you were soft banned for moving too quickly. The symptoms of not being able to get items from a pokestop and pokemon fleeing are exactly what happen when you are soft banned. It should only last a few hours, and for some they're able to fix it by simply force quitting the app.

If the game detects you are changing drastically varying locations too often, you will not be able to catch pokemon, and pokemon immediately run away when you do try to catch them.

This is most likely due to GPS spoofing or another cheat of some kind.

As you level up the Pokemon you come across have a higher CP (Combat Power). This means that they'll also be harder to Catch.

You can use Razz Berries (you can get these from Pokeshops) to have a higher chance of catching the Pokemon. Once you reach level 12 you also get access to 'Great balls' which will improve your chance of catching the Pokemon as well.

On top of this there are different ways of throwing your Poke balls which increase the chance of success. The Pokemon Go wiki has some more details on Curve balls and the different Poke balls available.

From my experience that means that you have lost connection to the game servers. This can easily happen when you switch from home wifi to cellular network or kept the app open for some time (maybe in the background).

Another indicator that you lost connection is that the spinning Pokeball in the upper left corner never stops spinning and never disappears, when normally it would appear only for a few seconds and then hide itself again.

Most of the time you have to close the app completely (long press "home" or "menu" button on Android or use the app switcher button and swipe it away, similar on iPhones) and then start it again to make it work again.