You cannot check your text messages online with any mobile phone provider. Be cautious of any scam sites which claim that you can download software or "sign in" to read your texts from a PC. It is only possible to check your texts from your phone, not by any other means. However Verizon will allow you to check the number of messages you have sent, so you can see how much you will be charged, or if you are still in your text quota. To do this simply log into "My Verizon" with your account details on www.verizonwireless.com/b2c/index.html
Then click the messages tab where you can see how many texts you've sent.
The only exception to this is MMS messages (typically those containing an image) which may, if your phone does not support them, give you a link to a website where you can view the message and picture. You will know that you have a MMS message because your phone will receive a text from your mobile phone provider (e.g. Verizon) giving a link to their website will a unique URL which must be entered to view the message.
Some phone software will allow you to "back up" and save your text messages to your PC, so if you need to have quick access to read any of your texts from your computer, then see if your phone supports this feature. For example the iPhone has a number of third party solutions which can be used for backing up and viewing texts on your computer.
The only exception to this is MMS messages (typically those containing an image) which may, if your phone does not support them, give you a link to a website where you can view the message and picture. You will know that you have a MMS message because your phone will receive a text from your mobile phone provider (e.g. Verizon) giving a link to their website will a unique URL which must be entered to view the message.
Some phone software will allow you to "back up" and save your text messages to your PC, so if you need to have quick access to read any of your texts from your computer, then see if your phone supports this feature. For example the iPhone has a number of third party solutions which can be used for backing up and viewing texts on your computer.