The "rule" is that your rent should be no more than 33% of your monthly after-tax take-home pay.
I live in the NW section of DC, nice area near the Cathedral/Cleveland Park. I found a nice, cozy studio for $910/month, and I feel like I got a really good deal. Most studio apartments along Connecticut run for $1100-$1800/month. Deals of course can be found in the NE and SE (Capitol area, not across the river) corners of DC.
Edit: I sold my car when I moved here and do fine without it.
Edit: My combined gas+electric bill is around $25/month. Add another $35 for Verizon DSL. I don't have cable TV. I ride the Metro to and from work everyday and spend about $75/month for that.