Does the Sony PlayStation Portable (PSP) support PPPoE?
Simple answer, yes!

How do I configure the Sony PlayStation Portable (PSP) to connect via PPPoE?
1) Scroll left on your Desktop menu to "Settings"
2) Scroll down to "Network Settings" -> Press the "X" button
3) Choose "Infrastructure Mode" -> Press the "X" button
4) Select "New Connection" -> Press the "X" button
5) Press the "X" button -> Type in a connection name -> Select "Enter" (twice) -> Press the "X" button
6) Press right arrow
7) Enter your wireless device's SSID, or Scan for yours (make sure your Wireless is turned on, switch on the left hand side, by the analog stick)
8 ) Press right arrow
9) Select "Custom" -> Press right arrow
10) Select "PPPoE" -> Press right arrow
11) Select "User Name" -> Press the "X" button -> Type in the username -> Select "Enter" (twice)
12) Select "Password" -> Press the "X" button -> Type in the username -> Select "Enter" (twice)
13) Press right arrow -> Select "Automatic" -> Press right arrow -> Select "Do Not Use" -> Press right arrow -> Press right arrow
14) Press the "X" button to save
15) Select Test COnnection -> Press the "X" button
16) Surf Away!

Are there any PPPoE Termination Servers that work with the Sony PlayStation Portable (PSP)?
Yes Fine Point Technologies has tested the PSP with their ServPoET PPPoE Access Concentrator