As a preface, I work at an Apple Reseller store. I don’t really have an interest in the company, but I’ve had to go through a lot of training on the products. Anyway:
First of all, I want to say that yes, a HD based system can skip. Not in the sense of a CD skipping (which really isn’t skipping either.) As earlier stated, the HD writes songs to RAM, and then periodically writes more. When the drive is under stress, (being jiggled), the hard drive won’t spin up and the RAM cache will slowly run down. Different models have different amounts of buffer (or cache, or skip protection). The 4G ipods, including standard and minis, both have 25 minutes of skip protection. The ipod photo has 17 minutes. I don’t have my spec sheets on the 1 and 2G but I know that had next to nothing skip protection. The best thing you can do if your skip protection runs out is to keep the unit still enough for it to write to RAM. Either stop and stretch, or hold it in your hand all steady-like. I do it with mine, and usually works pretty well.
I think that the iPod, and the mini, were both evaluated in the running surrounding by Apple during design. Though not designed for this purpose, I don’t see any long term damage with the many clients we have due to constant jogging of the unit. But I do know that you can get better results with them by putting it somewhere that doesn’t bounce much. Armbands are best (and unlike the post before by someone who said “While the iPod mini is not a flash based player, the micro-drives they use are better for running. This is probably why Apple makes an arm-band holder for the mini and NOT for the larger model.” Wrong. Apple didn’t make an armband for marketing purposes to more strongly push the value points of the mini. It is hard for Apple to justify 4G@$249 and 20G@$299, so they added a smaller case, pretty colors and market it as a go-all do-all. Several companies created armband accesories under agreements with apple before the product was even released, for the larger iPods. Marware probably makes the best. Ipod minis with the microdrive are probably better as far as excersize and skipping go (especially because of the lighter and smaller aspect), but big iPod will work just fine. Plus if you decide to go Forrest Gump, you would run out of music on your mini a whole lot faster. 
As for dropping an iPod. The highest we have ever gotten one to drop without breaking is 8 feet to hardwood with no case, and 15 feet to hardwood with an iSkin. The unit is pretty robust and the first thing to go is ususally the display. The drive in most cases will still function fine after a drop. {we had some returned units with bad buttons and the like, and didn’t know what better to do with them. Our drop tests were conducted under less that labratory-like conditions.] If you drop it lots, you can get a super duper case called the lily-pod, (I think that’s the name.), it has a rubberized interior with an anodized aluminum exterior, and it is water-proof to boot. You can acutally submerge it and it will play on. Drop it on your bike at 28mph and no problem.
I would say though, if you do get an iPod, and are going to run with it, get the Extended warranty. It’s only $60 and is cheap insurance in case anything goes wrong for 2 years. It more than covers the cost of a new battery if it dies, and if you do jack it up running, you will either have it fixed or replaced with a similar model (brand new) at no expense. You just can’t lose.