Not all computer games...but most. I spend most of my day on my computer, and a lot of that time is dedicated towards playing computer games.

So if you're wondering what are some fun - and safe - computer games for teenagers to play, then continue reading.

First, of course, you'll want to determine the type of game you're looking for. Are you hoping for casual games? Or games you'll have to spend money on? Do you want games that take up a lot of brainpower, or games that you can play while you're waiting for dinner? I'll do my best to cover a variety of games, but if you're looking for more information, leave a comment and I'll try to help.

Casual games

Casual games are quick and easy, and are generally free. I really enjoy playing casual games when I'm stressed out or bored. My favorite categories include hidden object games and arcade games.

Hidden object games are just like those "I Spy" books you used to read as a kid. There are several different settings and you have to find certain items before time runs out. These items vary, depending on the game, but most include finding things like butterflies, stars, bottles, drums, and general things that anyone would recognize. Also, sometimes you'll have a list of items, other times the instructions will say "Find all the toys in this level," and sometimes you'll be presented with silhouettes of different items instead of the name.
Hidden object games are a great source of entertainment, and they're safe for the whole family.

Arcade games are along the lines of running a salon, farm, or diner. Things like Diner Dash, Alice Greenfingers, and Cake Mania fit into this category. They're harder than hidden object games, and they do require more brainpower and a bit of strategy. They also allow more interaction than other games, allowing you to decorate your business or customize other aspects.
There are also other objectives in arcade games, like training to be a Jedi or abducting humans while piloting a UFO. I haven't actually tried those out, since they're not as popular as Diner Dash.
Again, arcade games - at least the casual ones - are safe for younger kids. And as I mentioned before, they also provide a bit of a challenge, which is enough to keep young adults' attention.

Other casual games

Board games, like Sorry, Monopolopy, and Scrabble, count as casual games. You can play these the old-fashioned way, of course, but you can also play them online.
There are sports games, racing games, adventure games, card games, puzzle games (you've heard of Sudoku, right?), and shooting games. All of these can fit into the genre of casual gaming

Are all casual games free?

No. Sadly. Many are, but others you have to pay around $20 for. Diner Dash, for instance, is hugely popular, so they're not going to let you get away with playing that one for free, although you can play some levels online.
There are also games like Kudos - a life simulation game - that cost money, and may in fact not be worth it, and there are games like Cinema Tycoon, where you run your own movie theatre, and it is a ton of fun and may in fact be worth the $20 you have to shell out. There are tons of casual games, some free, some not, and you have to decide which ones you want to play, and whether they're worth a bit of cash.

Not-so casual games - Part I: The free ones

The free games that can't be classified as "casual" are usually RPGs (role playing games). Now, some role playing games require a fair amount of money to play, like World of Warcraft, which we'll get to later. But others really are free, albeit with worse graphics and less players.
Astonia is one of my favorites. This game allows you to play free or to pay a monthly fee. It's an RPG and you can choose to be a warrior or a mage (which is a wizard). There are plenty of people who play - some friendly, some not - and it allows for an in-game chat. This means, of course, that you may not want your kid playing, or at least not without supervision, but a teenager should feel right at home. On the plus side, Astonia is one of the RPGs that doesn't show a lot of gore and doesn't have, or allow, foul language. There is also frequent moderation of the chat room, and you even have the option of blocking public chat, although I personally don't recommend this, as it's usually a good thing to be friendly with people you'll be interacting with.
Other RPGs are games like Bite Fight, a vampires-versus-werewolves game, or Runescape, which you can play for free if you'd like. As far as I can tell, Runescape is centered towards slightly younger players, and it is extremely family friendly.

Not-so-casual games: Part II - The ones you pay for

As I said before, World of Warcraft falls under this category. This is an insanely addictive RPG, which tons of people play. Also, I don't recommend it. Yes, it's fun, although it's also repetitive, but if you want to have a life, you'll stay away.
Then there's The Sims. Right now there are The Sims and The Sims 2, but if you wait until June 2, 2009, you'll be able to buy The Sims 3, which looks great. The Sims, as the name suggests, is a life simulation game. You create players, neighborhoods, houses, pets, stores, and more. You make the people do what you want (you can even kill them, which is so much fun). There is some crude humor, but The Sims is pretty much innocent and is tons of fun. I can spend hours playing, and I have already reserved my copy of The Sims 3.
The Sims, as well as some other games, is available on several platforms. Such games include Call of Duty, Fallout, and Halo. Those are three extremely popular games, but if you own a Playstation 3 or an XBox 360, you'll want to play them on that platform instead of your computer. Yes, they're popular on the PC as well, but they take up unnecessary space that you probably don't have.

So where do I find these games?

All over. But I'm so helpful, I'm going to give you a list of websites that should point you in the right direction.

One quick tip, however, before I let you go - on ArcadeTown, my favorite website for casual games, you have a chance to play the game for either 1 hour or 10 times (whichever comes first). There's a glitch, however. If you keep the game on your computer and do not turn your computer off, the game will not shut down. Thus, you can actually beat the whole game for free. I have done this many, many times. Just make sure that you do not exit the game or turn off the computer, and you can play for free! Aren't you glad you read this?