(Been sitting in drafts).
Technical questions about charging Lithium Ion batteries have, as their first answer "If you are asking this question you probably shouldn't do it" :-). There is an element of humor there, but also a lot of truth. Refernces to "some sort of IC to protect from overcharging" suggest that a modicum of learning is required. This can be great fun BUT is a necessity if you start producing your own LiIon chargers.
A number of people seem to have assumed that you wanted to up convert 500 mA at 5V to more current at less voltage - but I do not read it that way.
I assume that you are trying to use a USB port to charge and want as much current as possible - say 750 mA. The following addresesses that perspective.
A USB connection does not "output" current - it outputs Voltage, and current then flows depending on the load. This is an important and non trivial distinction even though it may not appear so.
The maximum current which CAN be drawn from a USB outlet depends on both its physical capabilities and the current which MAY or SHOULD be drawn depends both on the design of the port and the ability of your equipment to "negotiate" with that port.
So you have CAN, and two flavors of MAY.
Regarding "MAY" - Recent revisions to the USB standard allow up to 750 mA to be drawn from a USB port, but this capablity is not manadatory for the supplier to provide, and there is now a spec for chargers only, which can provide as much as 5 Amps !
This is subject to negotiation with the port
Here is a somewhat informal but practially useful discussion of using USB as a power source
POWER FROM USB:
The essentially trivial matter of drawing current from a nominally 5 Volt USB power supply is complicated by a large range of practical issues.These are summarised reasonably well in the following text. There is nothing technically hard here - just lots of little issues bundled together to help confuse.
See also this excellent related prior stack exchange discussion.
The following, relating to USB Power-Supply issues was copied directly from
The Wikipedia USB page
The USB 1.x and 2.0 specifications provide a 5 V supply on a single wire from which connected USB devices may draw power. The specification provides for
no more than 5.25 V and
no less than 4.75 V (5 V±5%) between the positive and negative bus power lines.
For USB 3.0, the voltage supplied by
low-powered hub ports is 4.45–5.25 V.
A unit load is defined as
100 mA in USB 2.0, and
150 mA in USB 3.0.
A device may draw a maximum of
5 unit loads (500 mA) from a port in USB 2.0;
6 unit loads (900 mA) in USB 3.0.
There are two types of deviceslow-power and high-power:
A low-power device draws at most 1 unit load, with minimum operating voltage of
4.4 V in USB 2.0, and
4 V in USB 3.0.
A high-power device draws the maximum number of unit loads permitted by the standard.
Every device functions initially as low-power
but the device may request high-power
and will get it if the power is available on the providing bus.
Some devices, such as high-speed external disk drives, require more than 500 mA of current
and therefore cannot be powered from one USB 2.0 port.
Such devices usually come with Y-shaped cable that has two USB connectors to be plugged into a computer. With such a cable, a device can draw power from two USB ports simultaneously.
A bus-powered hub initializes itself at 1 unit load and transitions to maximum unit loads after it completes hub configuration.
Any device connected to the hub will draw 1 unit load regardless of the current draw of devices connected to other ports of the hub
(i.e. one device connected on a four-port hub will draw only 1 unit load despite the fact that more unit loads are being supplied to the hub).
A self-powered hub will supply maximum supported unit loads to any device connected to it.
In addition, the VBUS will present 1 unit load upstream for communication if parts of the Hub are powered down.
In Battery Charging Specification,
new powering modes are added to the USB specification.
A host or hub Charging Downstream Port can supply
a maximum of 1.5 A when communicating at low-bandwidth
a maximum of 900 mA when communicating at high-bandwidth,
and as much current as the connector will safely handle when no communication is taking place;
USB 2.0 standard-A connectors are rated at 1.5 A by default.
A Dedicated Charging Port can supply a maximum of 1.8 A of current at 5.25 V.
A portable device can draw up to 1.8 A from a Dedicated Charging Port. ***
The Dedicated Charging Port shorts the D+ and D- pins with a resistance of at most 200 Ω.
The short disables data transfer, but allows devices to detect the Dedicated Charging Port and allows very simple, high current chargers to be manufactured.
The increased current (faster, 9 W charging) happens if both the host/hub and devices implement the new charging specification.
*** DCP now seems to allow up to 5 Amps.
This would happily destroy any standard USB connector.
See Battery charging V1.2 spec and adopters agreement DECEMBER 7TH, 2010.
Dedicated charging port
ie no data - just charging
MUST operate in dark grey area.
MAY operate in light grey area.
NB note that requirement for DCP is LESS stringent than CDP = Charging Diwnstream Port = data equipped downstream port,
which must maintain Voltage above 4.75V out to 1.5A.
Charging downstream port:
ie has data and charging capability.
MUST operate in dark grey area.
May operate in light grey area.
MUST exit light grey area via right hand side only - ie while providing between 4.75V and 5.25V current drain must increase through 1.5A.
After that any area in light grey is valid.