However, as I noted recently in "How to use external storage to expand unexpandable Android devices," you're not totally out of luck. Thanks to USB On the Go (OTG for short), you can connect flash drives to some smartphones and tablets, though it does require a cable.
That's not a particularly elegant solution, what with the cable hanging off the bottom of your device and a flash drive hanging off the cable. Enter Meenova, a small microSD card reader for Android devices. Born on Kickstarter, it's now available for preorder in your choice of four colors. Total price: $12.
As The Cheapskate, I consider that a really fair price for a gizmo that solves a fairly major issue with a lot of Android devices. Indeed, if you've balked at buying, say, an HTC One Mini because you were concerned it wouldn't hold all your music or movies, now you've got an easy and inexpensive fix.
The reader measures 0.8x0.9x0.3 inch, though it protrudes only 0.6 inch once plugged into your device's Micro-USB port. And it has a keychain loop and bundled snap hook so you can more easily transport it. You also get a Micro-USB-to-USB adapter so you can use the Meenova with a PC.
So, how much extra storage can you plug in? The reader works with microSDHC cards as large as 32GB and microSDXC cards up to 64GB. You can buy one of the former for around $20, the latter for around $50.
Sounds great, right? Now for the "but": the Meenova isn't compatible with all Android devices. Rather, it works with a couple dozen phones and tablets, include the latest HTC, Motorola, and Samsung Galaxy stuff and Google's Nexus tablets. See the compatibility list for a full rundown.
Assuming you have a compatible device, this is arguably the easiest and most elegant way to add a microSD slot (or even a second one in the case of something like the Galaxy S4). And for 12 bucks, how can you go wrong?