I have to chip in here (no pun intended). I've been using and destroying electronic components ever since I can remember and I've never had a LED explode. Granted, I've never attached one to 120VAC to see what it would do, but under logic-level (5V/3V) voltages with virtually unlimited current the worst I've ever seen is a little smoke and discoloration of the epoxy resin they're encapsulated in. I've seen chips and power transistors "pop their top" where a small piece of resin will fly off, but it's not at a velocity that would hurt someone. Anyway, it's more a situation of cracking than shattering; they're made to take a fair amount of abuse.

Digital devices are generally made to tolerate a +/- 5% variation in their supply voltage (5V) and an absolute maximum typically is at 6 volts. This means we're fine from 4.75 to 5.25V, and small spikes above that won't necessarily destroy the device. Rechargeable cells produce a nominal 1.25V, a little over 1.3V right off the charger and 1.2V after some use or idle time. Thus, we're looking at about 5.2 off the charger and 4.8 after some time. This is just fine, but we run into serious problems with alkalines which are sometimes almost 1.6V per cell. Even at 1.5V nominal, we're already at 6V-- bad news.

I've never seen a removable AA battery pack that was regulated. Any regulation will happen on the board of the device. Please just use rechargeables, and keep the DVM handy to double check polarity, voltage, etc. You're guaranteed serious damage if you hook things up backwards