It's still pretty common for OEMs to make 16GB the default storage option in phones, but you don't always have to live with that. If there's a microSD card slot, you can dump a ton of data on it—you just need to buy one first. Luckily, Amazon Goldbox has some killer deals on SanDisk storage products today only.
The deals on microSD cards are probably the most relevant to Android folks with a 32GB card going for $15.99 (52% off) and a 64GB one at $31.99 (51% off). The gigantic 128GB card is down to $99.99 (23% off). That's a lot of data for a phone—as much as some laptops. If that's not your speed, the SanDisk 64GB OTG drive is on sale for $29.99 (40% off) as well.
These are just the Android-oriented deals. You can get regular SD cards, SSDs, and standard flash drives on the cheap too. Remember, these deals are good for today only.