Others have suggested wireshark, which is an excellent tool, but somewhat cumbersome to use. You typically have to catch the traffic, transfer it to your desktop, and then take a look.
My most commonly used tool is ngrep, which combines tcpdump style packet filters with grep style filters on the packet content, and an output display style which is adequate for debugging most HTTP issues.
$ sudo ngrep -d tun0 '^(GET|POST|HEAD|HTTP)' port 80
interface: tun0 (10.104.1.6/255.255.255.255)
filter: (ip or ip6) and ( port 80 )
match: ^(GET|POST|HEAD|HTTP)
####
T 10.104.1.6:39700 -> 93.184.216.119:80 [AP]
GET / HTTP/1.1..User-Agent: Wget/1.14 (linux-gnu)..Accept: */*..Host: examp
le.com..Connection: Keep-Alive....
##
T 93.184.216.119:80 -> 10.104.1.6:39700 [A]
HTTP/1.1 200 OK..Accept-Ranges: bytes..Cache-Control: max-age=604800..Conte
nt-Type: text/html..Date: Fri, 24 Oct 2014 11:21:44 GMT..Etag: "359670651".
.Expires: Fri, 31 Oct 2014 11:21:44 GMT..Last-Modified: Fri, 09 Aug 2013 23
:54:35 GMT..Server: ECS (cpm/F9D5)..X-Cache: HIT..x-ec-custom-error: 1..Con
tent-Length: 1270....<!doctype html>.<html>.<head>. <title>Example Domai
n</title>.. <meta charset="utf-8" />. <meta http-equiv="Content-type"
content="text/html; charset=utf-8" />. <meta name="viewport" content="w
idth=device-width, initial-scale=1" />. <style type="text/css">. body
{. background-color: #f0f0f2;. margin: 0;. padding: 0
;. font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, san
s-serif;. . }. div {. width: 600px;. margin: 5em
auto;. padding: 50px;. background-color: #fff;. borde
r-radius: 1em;. }. a:link, a:visited {. color: #38488f;.
text-decoration: none;. }. @media (max-width: 700px) {. body
{. background-color: #fff;. }. div {.
width: auto;. margin: 0 auto;. border-radius: 0;.
padding: 1em;. }. }. </style> .</head>..<body>.<div
>. <h1>Example Domain</h1>. <p>This domain is established to be used
for il
I also recommend a more obscure tool called chaosreader available from http://www.brendangregg.com/Chaosreader/chaosreader0.94. It'll turn a tcpdump file into a browsable set of html and other files, showing you all the traffic in a very accessible form. Much easier than wireshark when you are more interested in the content of web communications than the breakdown into packets.