To be completely fair, moving your laptop around when it's off does damage, too.
Manufacturers know this and it's why they try for stiffer frames, rubberized everything, tougher LCD screens, strain relief on internal cables, and so much more.
When I was a computer tech, we would tell customers that a desktop generally has an expected lifetime of 4-5 years and a laptop 3-4 years. I've gotten well over that with both, but generally it's true.
A laptop will see a bunch of abuse, no matter if you have the most plush carry case in the world. The bumps, jolts, moving the monitor, setting it on a table, picking it up, everything you do to move it damages it in some slight (or not so slight) way. Plugging in cables is much more often in a laptop than a desktop and can cause loose sockets.
Being on top of a desk, in a bag, in a vehicle, or wherever is much more likely to see an accident, too.
This is why I would caution people against buying a laptop. It's more expensive and more prone to damage than a desktop, so do you really need a laptop? If you need the mobility, then yes, you need a laptop. Just be sure you understand and accept the risks first.
Moving it while it's on is just more potential damage than when it's off. Even solid state drives aren't 100% guaranteed against all damage.
Edit:
I've been asked how simply picking up and setting down a laptop can damage a laptop. Well, there's the strain on any plastic pieces as well as the hinges. Depending on how people pick up or set down the laptop, there's torque put on the case and/or mobo. I've seen instances where a laptop quit working simply because it was picked up. I've destroyed my laptop by putting it in my cars passenger seat too hard, and I didn't even drop it very far. (It was the first time I had done anything like that, but it was old enough that any jarring was probably going to break something.)
The reason behind this is because integrated circuits (aka: ICs, or chips) soldered on the board don't stretch and bend at the same rate the fiberglass circuit board does, so eventually you can separate the solder points by these stresses. Heat cycles can do the same thing (ICs and fiberglass expand and contract differently, too), and in fact the heat of running the laptop can weaken the solder joints to make it more likely to happen if you are moving it while it's running. Surface mount electronics are just barely attached to each other at the best of times.
The plastic in the case can eventually break, leading to the stress being picked up going to the mobo or other electronics, instead of the case. The hinges can fail, causing the LCD to fall and crack, or simply wear the wiring/cables going between the screen and mobo, eventually causing a short or a break.
You can find lots of examples of all this usually irreparable* damage by doing a basic Google search. Parts can be replaced, if you can find them, are willing to pay for them, and willing to replace them yourself or pay someone to do it for you. I've seen it happen quite a bit over the several years I was a computer tech, and several times since I became a programmer.
(*) People try to repair circuit board damage by reflowing the solder with an oven, hair dryer, or heat gun to varying success. Usually the repair is temporary, even if it's successful at first.
6When the laptop is suspended, doesn't the power shut off completely? The fans & hard drive all stop? Why wouldn't the drive should be as safe as anytime it's powered off? If the drive stayed powered on, the battery wouldn't last more than a few hours. – Xen2050 – 2018-09-18T04:48:51.707
4Read your laptop's manual about maximum acceleration values or contact the manufacturer. – Ipor Sircer – 2018-09-18T04:56:48.933
13Many laptops today have SSDs which don't care about movement at all. - That leaves the potential for overheating (as discussed in the answer by another poster). Side note: IT has happened multiple time to me that Windows with its excellent reliability ( ... ) did not go into standby when it should have and the laptop remained on. It never caused any harm - BUT I also wasn't running anything on the computer at the time. On idle, most laptops (especially small portable ones) are fairly cool-running nowadays. – DetlevCM – 2018-09-18T08:30:02.190
1Why not suspend? It changes nothing, and (on my laptop) it's as simple as pressing the Power button. [that is really easy to set up too] – Hobbamok – 2018-09-18T12:47:47.470
9You probably close the display lid, and that's enough to put it into sleep, anyway. Laptops are designed to tolerate much more than that, so no worries. Unless it's a sturdy business laptop, it'll probably die in a few years time no matter what, but not because of that. The two most usual death reasons are poor soldering on the mainboard [since we have to put up with lead-free solder, it's a constant problem in the whole electronic industry, aggravated by the unavoidable internal stresses of plastic houses) and mechanical failure of the display hinges. – Gábor – 2018-09-18T13:09:44.347
There are other answers that go into this but when you say, “However, out of convenience I'd like to not turn it off when travelling between places.” I am a bit baffled. A suspended modern laptop goes from lid closed to lid open in seconds. What fear of delay do you have? Even if you completely shut it down, is the minute or so really that irksome? At the end of the day you need to realize that hibernating any modern laptop—where memory is stored to disk as part of the hibernation process—effectively powers down your laptop and allows you to turn it on quickly. – JakeGould – 2018-09-18T14:07:49.390
1Anecdote: Like @DetlevCM, Windows did not suspend when I put my laptop in its bag. After a long trip, it came out fairly hot, and it seems like it was off due to thermal shutdown as the battery was still half full. So, to answer, no, it shouldn't cause any severe hardware damage as there are built-in safety features. I'd worry about any spinning hard drives though. – PNDA – 2018-09-18T16:00:47.310
A lot of the answers mention hard disks, which are long-obsolete but may be present if you're using an older or weirdly-configured laptop. If you know whether yours has one, you should mention it, since this affects the validity of the claims to some extent. – R.. GitHub STOP HELPING ICE – 2018-09-18T16:54:40.370
1@JakeGould there are still some buggy device drivers around that won't work properly after suspend & resume. Booting OTOH does take a significant amount of time, or certainly used to with hard drives – SSDs have fortunately changed that a bit. — More inevitable point though: even normal suspend will stop the laptop from doing what it was doing. Which is hugely annoying when you're running some simulation, or logging some remote server's responses, or rendering a movie, or cutting a live recording... first thing I do when setting up a computer is always to disable all auto-suspend vectors. – leftaroundabout – 2018-09-18T19:44:07.713
7@R.. You're being a bit quickly on declaring hard disk drives obsolete. Even if not a Mac since 2012 has had one, many if not most PCs, especially at the lower end of the market, still use HDDs. – jcaron – 2018-09-18T22:04:09.000
@jcaron I tend to agree with you, but will say that the statement R.. makes should be, “A lot of the answers mention hard disks, which are less and less common as primary booting devices…” The reality is hard disks for storage are cheap and getting cheaper all the time. While SSDs are great, their most practical current use is for primary boot devices on laptops and some desktops. In my mind, anyone still booting from a hard disk in 2018 really shouldn't. SSDs are very cheap and the system will get an instant speed boost by an SSD upgrade. – JakeGould – 2018-09-18T22:29:31.463
@jcaron: Even my $270 laptop purchased last year has SSD (eMMC). Windows has been unusably slow with HDD for quite a while now. If there are vendors still selling laptops with HDDs, they're targeting either ignorant consumers or ones who want very large sizes without paying for what SSD at that size would cost; normal-user sizes are dirt cheap in SSD. – R.. GitHub STOP HELPING ICE – 2018-09-18T22:31:09.027
@R.. The problem with your statement is it doesn’t address the division between storage cost and price and “…which are long-obsolete…” makes it sound like we are talking about AM radio or some other obsolete tech. Read my reply to jcaronabove, but the correct assessment is SSDs are less common as boot devices. For other storage hard drives still win in capacity and cost. – JakeGould – 2018-09-18T22:39:20.263
1Any moveing around of a laptop bears the risk of dropping and then damaging it, regardless of the standby state... – PlasmaHH – 2018-09-19T07:27:06.747
1@Hobbamok Every laptop I've owned has had the option to set it to go into standby mode when the lid is closed, which would be required when putting it into a bag anyway. There's literally no extra effort involved in that case. – Anthony Grist – 2018-09-19T15:29:18.593
1Funny note. For a while now I've been observing people walking around to meetings with their laptops open or closed. It's almost always open for windows pcs, but virtually never for a mac. I do think windows-10 has fixed most of the issues though, If you are paranoid of suspending you might want to re-test your assumptions after upgrading. – Bill K – 2018-09-20T18:42:22.700
Very early hard disks (c 1980) would be damaged if moved/shocked when running. A lot of development went into providing them with 'catchers' to prevent this (also for unexpected power downs) so any modern hard disk is pretty much shock resistant. – Rich – 2018-09-20T23:42:05.040
No one mentioned the additional wear on the battery yet. The battery has only so many charge-discharge cycles and keeping the device powered on (on batteries) when not in use wastes charging cycles; plus, draining the battery to low charge regularily, like <10% as in when the emergency shutdown kicks in, is extremely stressful to the battery and will yield significantly less useful life a.k.a. charge-discharge cycles. – JimmyB – 2018-09-21T10:43:22.960