The cause of lag and stream stutter is usually down to a connection speed issue somewhere along the lines, sometimes its at the source and sometimes its at the end users connection (the listener) and sometimes it is also the datacenter connection if there are hardware/connection issues its rare but it does happen. It can also depend on how your connection is routed.
To be clear here the source is the computer connecting to the Shoutcast server, ie the one you plug your mixer and microphones into

Connection Example from studio to datacentre
So in this scenario those monitors are your computer, where the music and shows stream from, you then connect to your ISP and your ISP will route the traffic to whichever datacentre the stream is hosted on. Its actually more complex than this but to keep this simple that’s basically how it works.
Datacentres are there for a reason, they have high-end internet connections both in and out, they have high end equipment to deal with people connecting in. A web server is pretty much a computer which has some software on and handles web pages, shout cast servers, mail servers, etc. Connections can handle heavy loads, they are designed for this purpose.
Your ISPs connection (Residential and low-end business), unless it is something like SDSL or Fibre-optics is not really designed for to many connections and thus if you hosted your own Shoutcast or IceCast server you may struggle to get many listeners without severe lag happening, the lag usually gets so bad that the stream sounds like its stopping and starting, or sometimes stuttering. The key is your uplink stream and this will effect your ability to not only host your own ShoutCast server but also to connect to remotely hosted ShoutCast servers.
An Analogy
Shout cast streams work in kbps which means kilobit per second, its simple a measurement unit of data. If your stream is encoding at 128kbps then your uplink speed needs to be at least that just to get your stream out. In reality it needs to be much higher because there will be other things running which need to take a piece of your total uplink speed.
Imagine if you had a reservoir of water and you needed to take out 128 litres a second, your machinery (computer) is more than capable and will try to draw 128 litres a second, it will even try to take the water at that rate when its physically not possible, but your pipes taking the water were only capable of taking 98 litres per second you will then start to bottle neck because the stream simple can’t fit through the pipes even though the machine is trying to pull it.
Another analogy is that your trying to fit a 128mm wide coin in a tube that is only 98mm wide, it simple won’t happen.
What affects the uplink stream?
Well… Pretty much anything using your internet connection, MSN, Web Browsers, Skype, Live Chats which have live connections/sessions, software checking for updates like Windows and many other OS will do automatically and there are many reasons as well. If you were to host your own website in addition then that would simply impede your connection speed every-time someone requested your website.
How would I get an idea of my uplink and downlink?
You can get an idea of your uplink and downlink speeds from sites such as those listed below:
SpeedTest.net
DSLReports.com
There are others out there you can search for.