I've done a few Arduino-like experiments using their Pi Cobbler breakout board. I got mine to output status information (date/time, IP Address, network stats) and/or a twitter feed on a cheap 16x2 LCD display. With a cheap wifi dongle and one of those USB emergency cellphone chargers for power, it's completely independent of wires, so I'm thinking about adding some motors and maybe a few IR sensors to create a basic rover. Once you get the distro setup to auto-login and install TightVNC server and enable SSH, you just need to give it a network connection to control it remotely from a PC. I only hooked mine up to an HDMI TV once on first boot to get those things running. Now I just turn it on and wait for the IP to appear on the LCD display and SSH or VNC into it.
I agree that initially it was tough to come up with useful things to do with it, but the Adafruit tutorials went a long way toward inspiring me and walking me through the more mundane details of taking care of the basics (SSH, VNC, WiFi, etc.) so that you can focus on actually doing something cool with it. You can also search around for BeagleBone or Arduino + Ethernet Shield projects for ideas since the Pi can do most of what those can at a fraction of the price. Good luck!