New member here, and I knew I had to join once I saw this question! Right now I'm responding via cell phone (a BlackBerry, to be exact), and while I definitely wouldn't use my phone as my primary source of RP, it really is a neat tool to have on your side.
I say this because I have my phone linked to my email account, which is gmail, so I get IJ notifications (comment rot nonwithstanding) whenever someone comments on an entry or gives me a tag. I think that's pretty handy. I also have AIM on my phone.
Personally, I use my phone for IRL stuff and RP stuff for the primary reason of staying connected when sitting in front of a computer isn't going to happen (like when I'm in class, or at work). However, when it comes time to thread, I'll find a way to make myself available for computer time.
All that said, even I will admit that I probably couldn't RP primarily by cell phone. For one, it seems like entries are much longer on a cell phone when they're really not. I type faster on a standard computer. Another reason is that with a four-inch browser window, there's something to be desired by way of viewing content. Also, cell phone internet is considerably slower than DSL or wireless (or at least mine is). My stance is: if you have a cell phone compatible to RP, use it for times when you can't get to a computer, or to keep up with tags/comments to remind yourself to handle later. Other than that, stick to the computer. Personally, I feel like it's common courtesy to thread with other players computer-to-computer. That's the way I did it for 6+ years prior to my smartphone, and it's the way I prefer to do it now.