I have done just this. After ADT refused to 'update' the installation I had done about 12 years ago, and wanted to charge me $800 or so AND continue to charge me the $50 a month for monitoring.
So, I junked their old (crusty and mostly non-working) system and bought all my own kit. You'll find you can *always* buy better than what they give you in their 'free' package anyway, and tailor it to your own needs. You can find a monitoring company for around $10 a month. My insurance company doesn't care who does it, as long as it calls the police, alarms for fire, etc etc etc.
So. Here's what I got :
Vista20p panel. It's what most 'big name' companies install, except YOU get to set the 'installer code' and the ability to change / add stuff you hook up to it.
Honeywell 6120RF keypad. You'll need a 'keypad' to program your panel. This one also takes care of wireless sensors.
Various door sensors, heat / smoke sensors, break-glass sensors, Pet Immune movement sensors.
Don't forget the siren :P
If you have a landline, you can hook it up to this panel and have it call your monitoring-company-of-choice when an event trips. If you don't, you can get wireless addons which call them via cell-phone.
All this stuff is easy to order, easy to physically install. The programming for the Vista20P is a bit arcane and reminds me of programming assembly from my youth, but a day or two with the manual and some judicious googling and you should be set.
One of my requirements was that it hook up with the z-wave stuff I'd started installing, and I'm a fan of gadgets. So I *also* bought some touch panels with pretty graphics and stuff on them. They're expensive, mind (about $400 a pop) and their z-wave capabilities were limited. I ended up not using them for that and got a Vera-lite anyway. The wife, however, likes them.. so I consider the investment worthwhile (they can also display security camera feeds).
Note: NONE of this stuff allows you to monitor without a contract to a company. If you want to do that, then you can buy the add-on daughter board for the Vista20P called the Envisalink3. Hook that up to your home network and it can send you mails and stuff when things occur. Also note: if you do that and your power goes out, and you don't have battery backup for the internet gateway it sends through, you'll uh.. not get notified.
All this stuff I bought from 'the home security store'. Which is a haven for DIY'ers. They have a very helpful forum, very helpful staff and their prices are reasonable. I bought my bits a year or so ago and I've been a very happy customer.
Links follow :
Vista20P : http://www.homesecuritystore.com/p-958-vista-20p-honeywell-vista-20p-security-system.aspx
Wireless Keypad : http://www.homesecuritystore.com/nsearch.aspx?keywords=6150RF
Touchscreen pads : http://www.homesecuritystore.com/p-2081-tuxw-honeywell-tuxedo-touch-screen-keypad-white.aspx
Glass break sensors : http://www.homesecuritystore.com/c-76-glass-break-detectors.aspx#Filter=%5BManufacturerID=7*ava=0%5D
etc etc etc