You can.
Go to menu > settings> sound & display settings> notification ringtone, choose one from the standard ringtones given. I have Tweeters and it sounds a little bird twitting when I get a voicemail message.
Or if you don't like what is offered from the standard selection, you can be adventureous can create your own ringtone. You can use the RingDriod app to create your own using a song that you've already downloaded, then SAVE AS Type: Notification, then rename your Ringtone and hit SAVE. It will ask you one last time if you want to make this your default notication? Yes, please! or No, thanks. Say yes and once you get a voicemail, it will play it.
That's it. I love that I can assign different people on my contact list with different ringtones. Per instance, when my mom calls it plays happy birthday, I kow it's mom without even checking. Which comes handy if I choose to ignore the call. Hee, hee. I am so not kidding. LOL!