After reading good question here, I consider getting a backup. It looks like most photographers use same-camera-type backup, like 2 DSLRs and duplicate lenses. That is too expensive for amateurs!
Also, I think to get mirrorless camera for being more light and small. It is possible to have the mirrorless as backup to the DSLR? How should I choose the mirrorless for that? Are there some problems with a combination like that? Also can the DSLR backup the mirrorless too?
As others have said - this is a personal and subjective issue.
Also, you have not said what camera(s) you use and this affects the decisions.
I am arguably "semi professional" (or keen amateur) making money on my photography but not as my main job. Despite what Stan says, a very keen amateur does NEED a backup camera when it gets to he stage that taking photos in many situations becomes a significant part of the life experience. I have travelled extensively in Asia on business in recent years, I take many photos in "tourist mode" while away and I would not dream of not having a backup camera at all times. I'd be "lost" with no camera at all.
For worst case situations having a good enough pocketable of any sort is fine.
I carry a Sanyo XACTO video + still camera which literally goes in a (large) shirt pocket and which will produce 3/4/5/6 Mp stills (I have a number of them) and MPEG video (VGA through HD depending on model). Image quality is good enough for record-of-trip purposes. The main losses wrt a DSLR apart for sheer image size and quality are speed of composure, shutter response and frame rate. A good DSLR will capture a pigeon that suddenly flits low overhead, a child suddenly seen in mid jump, a sudden gesture or multiple frames of an interesting activity. A P&S usually will not do any or all of these well.
BUT for "serious stuff" another DSLR is needed.
The more it has in common with your "main " camera the better.
Body: Usually lenses at least are interchangeable across the whole range of a manufacturers cameras. You can carry a D800 and a D2 and have the lenses match. Or a 5DMkII and an EOS350. The main differences are full frame to APSC and the lack of ability of some newer bottom end bodies to focus drive some non SSM lenses. Apart from such issue, a very cheap body can often be carried that still has excellent photographic capability. A leading edge camera will have more mp, better focsing, faster frame rate, better low light operation and more bells and whistles BUT a bottom edge 3 year old DSLR will usually take extremely good photos in most conditions. Not so long ago the top Nikon wedding cameras boasted 3 megapixels.
Lens interchangeability is so easy to achieve that it would be unusual not to have it. The 2nd camera acts as a lens holder for the first where top results are needed. See above re SSm/ manual focus drive and FF versus APSC crop issues.
Battery - it is a really really good idea to be able to share batteries as you need fewer chargers and can easily carry spares for either camera.
Memory card - the ability to use the same memory cards is also a good idea but this is not as vital as batteries or lenses. If the main camera uses SDHC and the older one CFG or whatever, pocketing say 2 x CF of moderate capacity will usually suffice and they can often be bought while away (usually at outlandish pries). If needing different memory cards be sure to be able to download either (flexible card reader or have the USB cable with you). Don't forget the backup charger.
Flash Usually compatible across bodies.
What I do (fwiw):
I'm working my way up the Minolta-Sony chain with the hope that Sony will even now make a real camera that comes close to the D700.
Sensors for the Nikon D800 they make but themselves they, so far, cannot save :-(.
(A900/A850 are fine on resolution but cannot see in the dark).
I have A77, A700 (died), A200 (sold), 7D, 5D, ...
These are 24 / 12 / 10 / 6 / 6 megapixel.
I thought about buying a somewhat newer backup BUT the 6 mp 5D doesa very good job. For most purposes quality is fine, body size is small, lenses are the same as the A77. Alas batteries differ and memory is SDHC/CF. So I carry 5D body with my "second most likely to be wanted" lens on it. Overhead is batteries, some CF cards and a charger. Not a lot of weight or room. 5D is worth to close to $0 to be worth selling so as a backup it serves a useful role.
As an amateur, you don't really need a backup camera, although you may want a second or backup camera. A professional has contracted to provide a service, and is legally responsible for mitigating all of the factors that may prevent him or her from providing that service. A wedding photog, for instance, can't simply tell the couple on their wedding day that they're going to have to reschedule because his shutter's stuck.
The point of same-brand (or same-type) backups is to carry as little as possible, and to ensure that as little thinking as possible needs to be done to adjust to the backup if you need to use it. Someone shooting, say, Nikon D4s as their main bodies may carry a D3/D3s or a D700 as a backup -- it'll be familiar, have the same field of view with the same lenses, and so on. A D7000 shooter might carry a D90. A Canon 1Dx shooter might carry a 5D. With things like flashes, it's more normal to carry the same model so that transferring settings is a no-brainer.
One doesn't usually carry duplicate lenses (except in highly specialised types of photography); having lenses that can, in a pinch, cover one another is more normal (that is, a mixture of primes and zooms covering the same focal length range). It's only when you have a signature "look" that depends on a particular lens that you'd carry an actual duplicate (usually) -- for instance, Ryan Brenizer without his 85mm/1.4 would still be a great photographer, but his customers wouldn't get the Brenizer look.
If you just want a camera for when you can't use the one you have now, and don't have to worry about getting immediately into the flow, then there's no harm in using a different type of camera. You may, in fact, want something different; something that's easier to have with you all of the time than your DSLR kit. (You may even want to have a couple of options, one of which may be a decent camera phone or compact camera.) Of course it's going to affect your post-processing procedures, but it's not like being dropped by parachute into a country whose language you don't understand and with one leg amputated -- you can adjust. It's only when your living depends on getting things right quickly that you really need to worry about it.
There is no single "correct" way to deal with a backup camera. The main thing is to have something as a backup...particularly if you're getting paid to shoot and/or if it's something that can't easily be re-created.
It is true that many photographers will use cameras of the same brand/lens mount. This is done to facilitate swapping lenses from the main body to the backup, but this is not required. The important thing is that your backup of choice can still get the shots you need to get, should your main body fail. It's really up to you and how much gear you're willing to carry.
Also: it's possible to save a little (actually: a lot) of money on a backup body by purchasing an older, used body from a reputable dealer.
If you're not charging money for your photography, the simple answer is that you don't need a backup.
That said, if you've spent a lot of time or money getting to a particular location or setting up a particular shot, it might make sense for you to have a second way of taking photos in case something happens to your primary way. Depending on your needs, that could be the camera in your phone. Or a point and shoot. Or an old film camera.
Once you start charging money for photography, you need to eliminate all possible sources of excuses. Backup equipment is one solution for equipment failure or loss.
I went on a trip to the Grand Canyon. First time I've ever gone there. I took a Canon dSLR, two lenses, and a Fuji X100. The point of the trip was not photography. It was to spend time with my daughter enjoying new adventures. If my dSLR had failed, I would have been disappointed, but it wasn't worthwhile trying to bring more equipment.
When I shoot a wedding, I have a camera on me, one ready to go in a bag my assistant carries, and one in my car. I have a lens or two on me, several on with my assistant, and quite a few more in the car. I could lose two bodies and still be fine. I could lose two or three lenses and still be fine. I could lose two flashes and still be fine. I could lose a tripod and still be fine. I more than double the amount of memory cards I could possibly need.
I don't want to be in a position where I have to explain any kind of equipment failure to a bride. If something had happened on my personal trip, so be it.
You mentioned that you're traveling and want to keep shooting if one camera breaks. It's generally useful to have a backup that can use your same lenses. It's really useful to have a backup that uses your same batteries. It's a luxury to have the same backup as your primary, because then you truly can keep going without having to skip a beat. If your backup camera is a "lesser" camera, then you'll always have a pang of regret of "what might have been" if you had your "better" equipment.
