Mobil Phone Charging:
Manufacturers claim that you should only use their chargers.

Proprietary charging interfaces:
Apple lightning connector
iPhone 5c and 5s and new iPads have "lightning" connectors for charging one end is a standard USB connector and the other is a proprietary connector.
The connector has a chip which indicates it has been certified by Apple.
Vendors have to pay Apple for this. Non-certified cables may give you an message saying it is not authorized, but as far as I know they still work. See iPhone battery - charging

"Motorola Razr:
The motorola Razr may give you an "unauthorized charger" message with third party chargers.

The USB specification limits the minimum power available from the interface voltage pins to 500 mA at 5 volts, or 2.5 W. The GSM version of the RAZR, which first adopted the USB charger cable, can apparently live with that, but the CDMA phone is more power hungry and needs more than 2.5W to charge. The chargers supplied by Motorola will deliver significantly more than 500 mA, and as a practical matter a lot of other USB chargers and interfaces will too, but with the latter you can't count on them to support more than the standard requires.

It may or may not still charge the phone, you'll have to try it to see. If it does charge the phone it will take longer to do so than a higher power charger would.
Source: Dennis Ferguson at www.wirelessforums.org

Another person said "I'm not sure that's all there is. My wife has a V3c, and I tried a Zip-Linq USB power supply rated 5V @ 1000 mA and got the same error message."

Had similar experiences with another phone and just kept exchanging them at Wal-Mart until one worked.

Cables:
See USB conectors

USB Mobil Phone Charge Cables
how-to make a usb battery
How USB charging works, or how to avoid blowing up your smartphone | ExtremeTech
Why Apple CouldnŐt Go to Micro USB Charging | Tech.pinions - Perspective, Insight, Analysis

Voltages:
Some devices can run from substantially higher voltages than the rating of their standard plugpack. This lets them deal with unregulated plugpacks whose voltage only drops to the rated figure when the plugpack's delivering maximum current. Don't bet on any particular gadget being able to do this, though. If you over-stress a regulator, it can easily overheat and die.
Source: USB Mobil Phone Charge Cables

Sample charging requirements:

Mobil Phones - radios
Motorola V330         5.9V 375 mA
Motorola RAZR V3c     5 V  500 mA
Plantronics Headphone 5 V  180 mA
Kenwood HandiTalkie  13.8 V 650 mA

Laptops
Apple PowerBook G4 24 V 1.9 A
Toshiba Portoge    15 V 2 A
Other Computer:
Card Reader HD      5 V 800 mA
LaCie Firewire     12 V
Canon PIXMA iP90 printer  16 V 1.8 A

Firewire 7-30 V

Other:
Canon ZR90 digital camcorder 8.4 V 1.5 A
Magellan eXplorist 500 GPS   5   V 1 A
Sony CD MP3 player           4.5 V 500 mA

USB battery power packs:
www.ladyada.net/make/mintyboost/make.html
www.usbgeek.com/prod_detail.php?prod_id=0347

Chargers:
Products page - Batterytender.com