Here in the US, we have a bafflingly complex mix of police systems, and consequently a thousand different SWAT systems. I'll start with what I know and zoom out a little bit, if it'll help.
Cory and Brett have already mentioned the two most common vans: the Ford Econoline, and the Chevy Van. In most police departments, this also doubles as the general-purpose van, so it's not usually overtly marked (it might have a police license plate, but that's it). This keeps it kind of stealthy. I remember driving through a bad part of Baltimore one morning on my way to the train station, and through sleepy eyes I could see that there was a van in front of me with the rear cargo doors open. And inside were a whole bunch of guys with ninja suits and submachineguns.
A well-funded PD might have a larger box truck as well, and the Grumman is probably most popular for this. This isn't an armored car by any stretch of the imagination, but it will haul a lot of gear.
A really-well-funded PD will probably have a "mobile command center", completely ignoring the GI Joe reference. These are usually large Class A RVs with lots of radios (which don't work), satellite antennas, floodlights all over the outside, and absurd numbers of lights and sirens. The idea is that if there is a Big Event, the MCC will roll up on the scene and give the important people somewhere to drink coffee and talk on radios that don't work, while wearing thousands of dollars in tactical vests and Corcoran boots.
And finally, some departmens have armored cars. This used to be pretty rare - the only people who got A/Cs were wealthy jurisdictions or ones with particularly insane sheriffs, but since 2001 there has been enough Homeland Security money thrown around that quite a few random jurisdictions have them. The V100 used to be the gold standard for SWAT, but in recent years there's been a boom in the number on the market. The Bearcat is a popular model, as well as the Grizzly. I guarantee you in five years you'll start seeing up-armored HMMWVs in SWAT liveries, too.