http://www.ebay.com/itm/321432521284
http://www.ebay.com/itm/131010822960
Are these functionally equivalent to tantalum capacitors or what should I expect different other than fewer bench fires? 
Those will work fine for the same required values.
Why all the fires?
Why not observe polarity?
The more you ruin things the more experience you get. 
They even shine like tantalums
LarryD:
Why not observe polarity?
+1'd you for that.
What do you want the capacitors for? Ceramic(*) caps are small and cheap for
their capacity, but are not very temperature stable, are microphonic (a bad
idea for an audio amp circuit for instance), and non-linear if used close to
the working voltage, and are very lossy. For decoupling they are perfectly fine.
(*) high value ceramics, many low-value ceramics use a different ceramic and are
much better behaved (used in antenna-tuning circuits for instance).
Some circuits are sensitive to the series-resistance (ESR) of capacitors (for instance
some LDO regulators have max and min specs for series resistance for their
decoupling capacitors). MLCC caps tend to have very low ESR.
These would be very useful for NRF24L01 power decoupling caps where I here very low ESR is desirable.
It could be you are seeing the failure of fake caps, bought from China on Ebay.
Foggiest:
It could be you are seeing the failure of fake caps, bought from China on Ebay.
Yeah, pretty sure I put the flaming cap in backwards. 
MarkT:
What do you want the capacitors for?
Mostly for on-board regulators such as the LM317, 7805, etc. For decoupling I use .1uF "normal" ceramics, not these multi-layer ceramics.
For the LM317, those monolithics will be fine... but that's definitely an application where polarity should be straightforward.. In any event, you've already learned the valuable lesson of which leg goes where. (Everybody should burn up a cap at least once, there's nothing more valuable than experience).
LarryD:
Those will work fine for the same required values.
Why all the fires?
Why not observe polarity?The more you ruin things the more experience you get.
Yup, those little ceramic disk caps are notorious for being polarity sensitive.
Tkrain:
For the LM317, those monolithics will be fine... but that's definitely an application where polarity should be straightforward.. In any event, you've already learned the valuable lesson of which leg goes where. (Everybody should burn up a cap at least once, there's nothing more valuable than experience).
Year and years ago (like, before the dinosaurs) I stuck a bunch of 1000 uF caps into the wall outlets in high school shop class (the shop teacher pulled the breakers and shut the room off at the end of the day).
Next morning, they all learned what reverse polarity, AC and overvoltage do to electrolytic capacitors! BWAHAAA!!
Krupski:
Year and years ago (like, before the dinosaurs) I stuck a bunch of 1000 uF caps into the wall outlets in high school shop class (the shop teacher pulled the breakers and shut the room off at the end of the day).Next morning, they all learned what reverse polarity, AC and overvoltage do to electrolytic capacitors! BWAHAAA!!
just hope that the teacher is not on here, you could get this noted in your permanent record !
If you can't handle putting in capacitors correctly, are you on the hunt for nonpolarized diodes and transistors next?
dave-in-nj:
just hope that the teacher is not on here, you could get this noted in your permanent record !
He has more chance of winning the lottery than that happening. .. esp when he did it before the dinosaurs!
polymorph:
If you can't handle putting in capacitors correctly, are you on the hunt for nonpolarized diodes and transistors next?
Non polarised diodes are easy to make. Just solder two diodes in parallel back to front.
Not much use for anything, except dropping an AC voltage by 0.7V, though.
You can get non polarised LEDs now, they call them light bulbs.
Non-Polarised power supply would fix all the OPs problems.
In all seriousness, they make a non-polarized Zener diode that is basically two Zeners reversed to each other in one package. I'm not sure why one of our customers puts one across his relays, but my job isn't to question the design, just stuff the boards accordingly.
Is it a Zener barrier for I.S. stuff?
Tkrain:
In all seriousness, they make a non-polarized Zener diode that is basically two Zeners reversed to each other in one package. I'm not sure why one of our customers puts one across his relays, but my job isn't to question the design, just stuff the boards accordingly.
But surely the forward bias of the one that's not "zenning" would defeat the object of the exercise?