Are you reading your Verizon e-mail with the Verizon webmail or a mail program on your computer such as Outlook Express?
If you are using webmail have you tried adding the addresses of the contacts you can not receive e-mail from to your address book?
Have you checked your spam folder for the replies?
Do the contacts at Yahoo or Hotmail get an error or bounce message back when sending an e-mail to you?
Can they send you new e-mail messages, but not reply to e-mails that you sent?
Can you not receive any e-mail from them?
Can you receive new e-mail from anyone else?
There is a Verizon E-Mail FAQ
here with several related questions and answers.
I hope the questions above help you find the answer to your problem.
If you have any additional questions please let us know.
Also, please let us know the solution to your problem (for example, you needed to add the contacts to your webmail address book) so that other people with the same problem in the future can benefit from finding the correct answer online.