Text messages, no. Voicemail, from any other phone, dial your 10 digit number, and when your greeting starts to play, press # and you should be prompted for your password, and can access your messages as you would with your own phone.
If there are people with whom you are expecting to exchange text messages, you can contact them to let them know of your plight by sending an e-mail to their text message address. For instance, firstname.lastname@example.org or email@example.com. Of course you have to limit the message to text-message length.