Well he's offline now and I doubt I'll wake up before he heads out. This is about all I know about storm drains. I don't know how accurate it all is but it's better than nothing right?
The part of the storm drain system you are looking at is called a
catch basin. The two I know anything about curbside ones and grated ones, and to be honest, they may be the only kinds because that's all I've see.
Curbside ones look like this:
http://www.jensenprecast.com/products/pdf/sewer&stormdrain%5Ccurbinletcatchbasins/cig2-48_b.pdfThis one has a 2 to 3 foot gap built into the side of the road. The gap in the front is around 5 inches high so you obviously can't get in through that. However they have to get cleaned out several times a year so there is an access hatch on top.
As you can see from the diagram the basin probably won't be much bigger than 2 or 3 feet squared.
The other kind is a grated basin. It looks like this:
http://www.jensenprecast.com/products/pdf/sewer&stormdrain%5Ccurbinletcatchbasins/dig2p-42_a.pdfSame deal as the other one. You'll usually see these ones built on the actual property. Their basins are actually sized based on the lot; a bigger property will either have more basins, bigger basins, or both. I can't imagine it being much bigger though. The curbside ones are a bit more consistent because roads pretty constantly sized.
In tight urban areas these will drain to a central line which will
possibly get processed (we're talking flowing through wetlands that drain into a river, not all those blenders and mixers you see in cartoons and movies) before flowing into the watershed somewhere. I'm sure plenty of cities don't even bother treating the water and just dump it straight into a creek, oil and chemicals included. In some areas they may just drain to a retainment pond. If you've ever seen a tiny pond with a corrugated pipe sticking out into it that's what it's for (in addition to firefighting). The storm drains actually drain into this. Some subdivisions do this too. In that case your exploration would end pretty quickly because you'd hit daylight at the pond, no other direction to go.
I can't imagine that you'll get far.
Here's a cross section of a catch basin:
http://www.tpcg.org/drainage/images/catch-basin_large.gifThat pipe is, at maximum, 18 inches in diameter. I can't fit through it, but maybe you can. :P
http://www.ba-mfg.com/images/catch_basin.gifHere is a local diagram of a catch basin. As you can see the manhole would be more interesting to go down. The big pipe would probably be the most interesting, although all the pipes leading to it are probably between 15 and 18 inches in diameter so there's probably no chance of getting into one.
As for potential dangers, there's flooding, getting busted by the law and your friends being richards and putting the grate back on top while you're inside it. I'll just elaborate on the first two.
It's possible that a storm drain where you are could fill up from water from the other nearby storm drains. I don't know if you can get water from the other side of the city in your storm drain, I hope the pipes are graded, but keep that in mind too. You don't need a lot of grade to keep water flowing in one direction, maybe 1/4 of an inch for 12 feet or something, so it's possible that if there was a sufficiently large amount of water coming from one direction it could flow up the pipe and into your basin even if it were graded.
It's probably illegal too, don't be fooled into thinking just because a catch basin might be on your property it belongs to you and you can wander all around the pipes. I'm sure you're not worried though.
Now you probably know more about storm drains then you ever wanted to know. If you're going to do it anyway then have fun and try not to drown, basins have grates on them for a reason. Take some pictures.
