There are two main types or power-up: Single Use and Upgradable. Single-Use are ones that are activated either by you, or are activated in the background automatically. Upgradable power-ups are the ones that you collect while on a run. These can be upgraded in the Shop to make them more effective. You can also purchase Coin multipliers using real money.
See below for more information on the power-ups available in Subway Surfers:
This is by far the most useful power-up, as it effectively saves you from death. You will earn plenty of these in your travels, but it's worth buying them every now and then as they come in handy for completing certain missions.
To activate the Hoverboard, double tap the screen. You will then be on a hovering skateboard, and, should you hit an obstacle, you will simply lose the Hoverboard and go back to running.
The Mystery Boxes can be purchased in the Shop and collected in game. They are chiefly the way that you find the parts required to unlock new characters, as well as other goodies. Currently the prizes on offer in the Mystery Boxes are as shown in the image below. Notice how there are tiers of rarity.
Free on a run, or 500 Coins in the shop.
These are the items you can get in each Mystery Box
This increases your Multiplier by 5 for a single run. It is an expensive power-up, but if you have lots of Hoverboards saved up and are planning that epic, high score-beating run, then equipping the Score Booster is a great idea.
The Mega Headstart allows you to skip ahead by 1,000 meters on a run. It is useful for completing various missions, as well as for giving you a breather and a healthy-dose of points at the start of a run. Once you purchase it, Headstarts appear in the bottom left-hand corner of the screen and you simply tap them to activate.
You will have as many of these available to purchase as missions you have oustanding. They simply allow you to move on past one mission and proceed to the next, if there's one that you think is going to take you hours of work to achieve.
The Hoverboard is vital for getting high scores
As mentioned above, the power-ups below can be found dotted around the subway on each run. You can increase the length of time that each one lasts by upgrading them in the Store.
This is a really fun power-up whereby your character uses their spray cans as a jetpack. They ascend above the tracks and can avoid all obstacles, essentially skipping ahead while still earning points. In the Shop you can upgrade the Jetpack, for a few which increases from 500 Coins upwards depending on what level your Jetpack is already. The upgrades increase how long the Jetpack power-up lasts for.
These allow your character to jump far higher than normal, as if they have springs on their shoes. By upgrading them in the Shop you can increase the length of time that they last for. The Super Sneakers are generally useful for bypassing trains - you can jump right over them if you time it right, and allowing you to spend most of your time in the air - where it is safest to be.
This is a great power-up which draws in Coins from the lanes around you. The good thing about this is it saves you from having to change lanes, meaning you can focus on avoiding obstacles rather than collecting Coins. As with most of the other upgrades, you can increase the duration of the Coin Magnet in the Shop.
The 2x Multiplier is great for getting some massive scores. Once you pick it up, every Coin you collect will be doubled for as long as the power-up is in effect. This is why it's a good idea to upgrade your 2x Multiplier in the Store - to make it last longer.
The Coin Magnet is a good way to maximize the Coins available on any section of a run
UPDATE: Power Jumper
The Power Jumper allows you to jump even higher than you were previously able to using the Super Sneakers and collect any Coins that might otherwise have been out of reach. This can also allow you to access routes on rooftops and on top of trains more easily.
Some rooftops are only accessible with the Power Jumper. It is very similar to the Super Sneakers but can only be used for one jump. It is often positioned near to a roof or tunnel that contains Coins on top, allowing access. However, you must be careful when using it as you can find yourself on top of a building when you would rather be below it collecting all the Coins.
It also takes a lot of getting used to in terms of the landing, so use it wisely. You are not able to upgrade the Power Jumper. The Power Jumper was introduced with the Beijing edition of Subway Surfers: World Tour.
Premium power-ups are those which you can only attain by paying real money for them. Surprisingly, there is only one of these in Subway Surfers.
This does exactly what it says. For a modest fee, you can double all of your Coin pickups. This gives you a real advantage against other players, meaning you can upgrade all of your other power-ups fare more easily. The question is, are you willing to spend real cash on it, as opposed to the imaginary Coins of Subway Surfers?
Power-ups can be picked up during play, and may have a profound impact on your success in any particular run.