Your contract of employment should give details of how much notice is required - if in doubt, an informal discussion with HR may clarify this. You are expected to stick to this - although how important it is depends on the responsibilities of your job, and whether your post can be filled by someone else.
There are several potential pitfalls with not working your notice:
1. It's unprofessional. You risk not being able to get a recommendation from your current employer in the future, or even worse, your current employer may mention this unprofessional behaviour in any letter of reference. Do you really want a new employer to get a letter like:
"Dear Mr. Doe, Thank you for enquiring about Mr. Between. I can confirm that he worked at ACME computers from September 28 2008 to July 13 2009 at which time he breached his contract of employment by refusing to work his notice period." It's unlikely that this would happen in an informal job, but in more professional jobs it can happen.
2. Your current employer may throw you out as soon as they get your notice of resignation. However, if you write that you are giving x weeks notice and that you are prepared to work for the full period - even if they throw you out and tell you are finished - they must pay you your full wages for those x weeks.
3. If your leaving without notice screws your employer over they can potentially sue for damages - e.g. if they have to go to an agency to get a temp to fill your post - the hourly rate for agency staff can be much higher than a formal employee - they could easily sue you for the difference.
Although it doesn't really apply in your case, I have seen people get absolutely screwed over because they treated an employer unprofessionally. I know one guy, an MD, who was coming towards the end of a fixed-term contract and was looking for a new job, with the full knowledge and blessing of his current employer. He got offered a good job, and his current boss gave him a glowing letter of recommendation. Then he decided, 'f*** it - I'm not staying for my 3 month notice period' and basically told them 'I'm off in a couple of weeks. See ya'. Of course, he left his current employer in the lurch. His old boss was furious, and actually wrote to the new employer withdrawing his letter of recommendation due to unprofessional behavior, and also wrote to the medical licensing board. The new employer after the recommendation was withdrawn, withdrew the offer of employment, and with no one to turn to for a recommendation, he was basically SOL. Then just to make it worse the licensing board, called him up in front of a formal disciplinary hearing, and gave a formal written warning for unprofessional behavior, and stated that if something similar happened again, they would cancel his medical license.
On the converse, it's common courtesy to tell any prospective employer about your notice period. It would be a standard part of the negotiations when they offer you the job. That's why prospective employers ask when you can start - they know that it's professional courtesy to give notice to your current employer. When I last went applying for jobs, I actually put 'Notice period: 3 months' on my resume. It didn't hurt my chances and I'm sure my new employer appreciated knowing even before inviting me to interview that there would be a delay before I could start.