Please read first
Account Security Recommendations on Steam Support Wiki!
To avoid being scammed keep your Steam Account details secure, do not disclose the Account Name and Password to any person or web site at any time.
The only exception when you could disclose your Account Name (only the Account Name, nothing more) is when you are being assigned admin on a game server. But you have to be sure that the person assigning you is who he claims to be before telling him or her your Account Name.
To avoid being hacked make your Account Password long and complex, mix small and capital letters and numbers.
Keep your computer secure, scan your PC with antivirus and malware removal programs regularly.
You should also use different contact e-mail address for your Steam Account from the public ones i.e. the e-mail address you use on forums and messaging services for example.
Never click any links that are sent to you in chat by strangers!
Never let any web site install anything on your computer unless you have requested it or you are sure of what you are getting.
Before accepting chat request from a stranger check his/her account (see "How do you recognize scamming?" below), if the account looks suspicious do not accept the request. The chat request may come from already stolen account and it may not look suspicious. If a person that you do not know sends you links in chat, terminate the chat immediately, never click any links that are sent to you by a person that you do not know (this applies also to messaging services and e-mails).
It is suspicious from any of your friends to send you links on chat without greetings and minor chit-chat first! Do not click any links right away, develop some conversation first to check some facts that your real friend would know, but not so many others, and see if you recognize your friend's writing style.
How do you recognize scamming?
The usual pattern seems to be such, that the scammer joins a public group on Steam and starts bombing the members of the group in chat with links for
free games or threats that your account will be disabled if you don't
verify your Steam Account details on provided link. The pages that you are directed to will have registration forms where you are asked to fill in and submit your Steam Account details - don't do it!
Check the scammer's account - it is usually named something like "Support Valve", "Admin VAC" or just some random letters and numbers; there are no details published about him/her on the account ("This user has not yet set up their Steam Community profile..." or "No information given. This profile is private."); there are no games on the account; the scammer goes offline immediately after sending you his lines.
The scammer may be using a stolen account with nothing suspicious to note, may be one on your friends list. You have to be sure with whom you are communicating, you never tell anyone your account details anyway and it is suspicious of anyone to ask you or direct you to a site that ask you this.
How your account may become hacked
The longer and more complex password you have the longer it takes to crack, they give up and move to next target.
Depending on your browsing habits, activity on messaging and torrent clients, e-mail safety etc. you may have different malware on your computer, some of the malware may spy on and disclose your Steam Account details.
If you have disclosed your Steam Account Name and e-mail address (for example on Messenger they can see your e-mail address and if you tell them there your Steam Account Name) they can request password change or reminder for the account and intercept e-mail from Steam Support to get the password.
When you click links received in Steam chat, messaging services or e-mails, you may be going to a site that has malware waiting to get to your Steam Account. The site may request you to install or accept something, decline and close the browser. If the malware causes unexpected or erratic computer behavior restart the computer in safe mode (press F8 repeatedly before Windows starts loading and select "safe mode" from the list). Scan your computer with antivirus and malware remover immediately, do it even if you have already lost your Steam Account.
What can happen when your Steam Account gets stolen?
Usually the stolen accounts will not be used, not immediately anyway, the only time the thief logs in to your Steam Account is when he/she changes the Account details to his/her own. Keep in mind that he/she can change all the details except the Account Name (and the Steam ID for that matter), Valve does not allow changing of Steam Account Name!
Your Steam Account can be used to
test cheats in games, to see if
Valve Anti-Cheat System (VAC) can identify those.
If your Account is caught cheating by VAC, Valve will ban the Account from all VAC servers for all the games using the same game engine as the game that they caught the Account cheating on. If cheating happened on HL2 engine game the Account is banned from all VAC servers for all games that use HL2 engine.
The VAC ban is a lifetime ban, Valve will not unban it, they will not even answer if you send them such a request - the Account becomes virtually useless!
Your Steam Account can be used for
further scamming and hacking.
Your Steam Account could be
sold to somebody. Valve has prohibited selling of the accounts, but it cannot control it. The rare accounts from starting days of Steam are in some sort of demand, because the Account Name could be a 4 to 8 digit code or an e-mail address.
There is probably certain number of accounts that will not be reclaimed for a long time or ever - abandoned or forgotten accounts (I had my previous account inactive for about 2 years before TF2 was launched for example, now one of my kids is using it), owner is not capable of submitting a support ticket to Valve correctly and has no one to help him with this, owner has lost proof of purchase.
What should you do when your Steam Account gets stolen?
Please read first
How to Reclaim a Hijacked Steam Account!
At first opportunity
create and/or log in to your Steam Support Account.
Submit your case to Steam Support (see the links below),
follow the instructions on how to fill in the report to the letter! If you did submit the case correctly you will receive e-mail with support ticket number shortly after and this will also show on your account on Steam Support page. This means that Valve has accepted the case and will be dealing with it.
If you do not submit the case correctly you will not receive the support ticket number. This means that Valve will not be dealing with it. Submit the case again and try to follow the instructions on filling out the form exactly!
Contacting Steam Billing and Support.
Providing Proof of Purchase.
Valve will reset your Account Password and e-mail you a new password, this will also show on your account on Steam Support page.
I would assume that Steam Support is working normal office days and hours, but there is also time difference between Europe and America (Valve is based in Washington state), UK is ahead of them by 5 hours and Finland by 7 hours for example. Minding previously written, if you submitted your case to Valve on weekday you should get your account back the same or the next day, but don't expect any answer until Monday afternoon if you submit your case during the weekend.
Log in to your Steam Account with the same old Account Name and the new Password that Valve has sent you.
Edit the Account settings to your own.
Read the first part of the article again to keep your Steam Account safe in the future.
Additional information:
List of free Steam games. 
