Cyanogenmod has tcpdump installed. You can run it from the shell, just make sure you select the correct interface:
tcpdump -i tiwlan0 -vv
Or, you can write the dump to a file on your sdcard, and analyze it with Wireshark on your desktop later:
tcpdump -i tiwlan0 -w /mnt/sdcard/tcpdump.out
There is also software like Shark for Root, which will capture the packets like tcpdump (it requires root, but does not require tcpdump, which is available on my Cyanogenmod 7.1, but I'm not sure if it is available in all versions of Cyanogenmod).