I agree to 10 points of Vikas however from security perspective I have to tell you few points that you must be careful.
I will try to keep as simple as possible. And here I simplify the technical stuff to your special case.
Firstly tokens are used to prevent Cross Site Request Forgery attacks (XSRF). Keep that in your mind. If there is a web platfrom without unique tokens on the forms then any attacker can force the user to make malicious requests.
If you simply try to authenticate the user with a token, this is pretty wrong. Because there must be no simple authentication process and you can not rely on token.
Here is how the login system works in official security documentations, im writing as I remember:
Identification: you have to identify the user firstly, that is generally done with username. YOu will know that there is a user exist in your system.
Authentication: Let's say you have already identified that user A want to login. So you mast authenticate the user A with something that you know and user A know. We call it password simply :) You cannot by pass this step with plain text methods. Passwords are generally encrypted in your db and also through all communication with secure certicates, check ssl.
Authorization: okay you made the authentication somehow, the user has a right to get Authorization. Let's say if the admin type user is logged in, he has differen rigts and if the normal user is logged in then she has regular rights.
Session control: finally you have to control the session with a secure way. Here generally in web applciations people use access tokens for all requests to be sure that the authorized user is aware of the request. As a platform owner you are responsible to secure everything until the session ends. If you don't satisfy the users with your security, then probably your platf is not going to survive longer.
Tokens have different lifetime to expire and different access rights.
Now let's look at what facebok like companies do with mobile aplications. For the mobile app they generate a unique access token which is alway alive. One shortcoming here is, if any attacker steal the mobile token generally she can do anything in the account anytime :) Anyway here our point is how they verify the users with those tokens; firstly the token is unique for that device. (Actually not exactly unique or not dependent on hardware, because if you clearly steal the necessary files from the device then you can use it on another phone). So with this unique access token which is generated with users password at their initial login on mobile app, they can login always automatically with that. And this method is a little similar to what you want to do. However pay attention that they don't authenticate the users with links or email code.
Verification is not an authentication, don't forget that. By sending e-mail you can verify the users if the emailed code is unique and valid for only 30 sec or 1 minute. I hope you got the point.
Here I suggest you to check single sign on across multiple domains, which is really interesting.
Single Sign On across multiple domains
Let's say you are logged in to google.com and then you visit the youtube.com Opps the youtube is already logged in? Yea, cool right, but exist for long time. They can authenticate users accross domains which use different cookies with a little and secure trick. You will read on the link.
If your service is not really confidential and if you want to make your users happy with easy login system. Here is two of my solutions which I love :)
1-) Ask users their email address: just directly send 4-6 digit code as e-mail. Ask user the enter/click on that. There will be no password at all, only unique code on each login.
2-) Let's say you need to verify the user with a stronger way than email. Then mobile phone :) Here trick is; you will not send the verification code to user, but they will send what you tell them to you.
Ask to user to send a SMS with a unique CODE to XXXXXX your number :) Connect your mobile operator with your web service and check whether the code is sent to you by the user :)
There is always a trade-off between security and simplicity, and also with complexity. You have to find the balance.
Don't try to make it simple if your security is going away.
Don't try to make it complex if it'll seem more secure.
Hope those informationn help you.