It depends on how much storage you need IMO. I've done several multi-month trips where I generate over 1TB of photos and video. For those I take 4 Western Digital portable 2tb drives. I make 3 copies and one is a spare that I have music, tv shows, etc. on but that I would erase if one of the other drives went bad. This used to happen to me regularly, but hasn't in several years. So maybe the drives are more robust these days. Why 3 copies? If/when one goes bad you'll be plenty nervous only having one copy.
Each day I dump my flash cards from each camera onto my SSD drive sporting laptop. I make a folder like
2014-10-10 Petra 5D3W
The W is for Wide and is from my camera with the wide glass, I have another for L for long lens. I have one for each camera, pocket camera, cell phone, you name it. If I see multiple sites in a day I try to make a folder for each one, though that doesn't always happen. This makes it possible for me to quickly drill down through my archive and quickly find what I need even without keywording my photos.
I used to cull photos daily before backing up, but it takes so long to back them up, the most I do now is quickly go through and pick a few selects that I might show to travel companions, or upload to social media. Most places in the world have horrible internet, especially upload speed, so backing up to the cloud is only possible with your top selects.
I then copy my photos from the laptop to my 3 drives, then delete all but the selects from the laptop. Next I ALWAYS have 1 of those drives with me, on my person when I leave the hotel room. Typically it's in my pants or shorts pocket. Maid robs the hotel room, or a thief, or hotel burns down, or bombed, or floods etc. you still have your pictures with you. Of course if you get robbed you lose a copy, but in my mind there's less chance of that than something happening in the room. If you have a companion, for instance my wife, she carries one drive in her bag and I do leave one in the hotel, preferably in a safe, unless it's a travel day. On a travel day I still keep one drive in my pocket, then the others in a backpack, but not together. Yes it's easy to stack them together, but if there's a shock or something bad that's going to hurt one drive, it could well damage both. Even different parts of the same bag is better than together. If I'm going to be going somewhere in a boat I put at least one drive in a ziploc sandwich bag. Scoff if you will but if you get late in a big trip, have a month or more of your life stored on this little thing, are on some 3rd world ferry or tiny canoe somewhere, you'll start wishing you had a simple ziploc bag.
Now if it's a smaller trip to a safe part of the world where it is all going to fit on my laptop SSD drive, then I leave it on my laptop, and make 1 backup copy to a portable SSD drive. I then keep that SSD drive with me at all times. Those are starting to get cheaper all the time. They're also smaller and lighter than traditional portable hard drives as well as faster. A few more generation and they'll be over 1TB and much cheaper and I can ditch rotating media forever, but not yet for a big trip.