An active HDMI to VGA adapter would be much better quality than and active Composite video (RCA) to VGA adapter. Both would be much more expensive than a passive adapter however.
Active HDMI to VGA adapters
A quick check using google shopping suggests that an active HDMI to VGA adapter will cost around £50 ($80) and should support 1920x1080 resolution if your VGA monitor does.
Passive Composite video to VGA adapters
You might be able to buy or make a passive adapter for a few pounds (dollars), unfortunately it would not split out the chrominance and luminance information, so at best you would end up with a monochrome image, and that assumes that your monitor is capable of taking a composite video signal on one of it's colour channels (usually green), which is far less common today than it once was.
Active Composite video to VGA adapters
A similar check on an active Composite video to VGA adapter reveals that they are available, but are more likely to be around £100 ($155) and will at most up-scale 480i or 576i video to 1920x1080 resolution, so the actual resolution will be either 640×480 or 720x576 at a lower frame rate.
Cheap Active HDMI to VGA adapters
An answer to a related question suggests that active HDMI to VGA converters can be had substantially cheaper (i.e. £13!) direct from manufacturers in China, but also reveals that people have reported problems with long term use of these kinds of devices:
Note that any conversion hardware that converts HDMI/DVI-D signals to VGA (or DVI-A) signals may come with either an external PSU, or expects power can be drawn from the HDMI port. In the latter case there may be a problem, as the HDMI specs only provide in a maximum of 50mA (@ 5 Volt) from the HDMI port, but some of these adapters try to draw up-to 500mA, in case of the R-PI there is a limit of 200mA that can be drawn safely, as 200mA is the limit for the BAT54 diode (D1) on the board. Any HDMI to VGA adapter without external PSU might work for a time, but then burn out D1. The solution is to either only use externally powered converters, or to replace D1 with a sturdier version. Also notice that the R-PI's power supply also must be able to deliver the extra current.
Looking for an active adapter with an auxiliary power in, I did find this one, which appears to have an mini-usb, presumably for power.
Given these prices/problems, you might be better off going out and buying a cheap DVI or HDMI monitor. In the UK you can buy a small unbranded screen for around £80 ($125) at the moment, if you look around.
Update for Raspberry Pi B+
According to the Raspberry Pi blog, Gert’s VGA Adapter allows you to use a VGA display with the Raspberry Pi B+ at the expense of most of the general purpose I/O pins. It even allows you to use the VGA screen in addition to the HDMI.
The colour depth is only 6 bits per channel (262144 colours in total), so there is noticeable banding, but if you want a cheap solution, and don't mind soldering a few resistors and through-hole components, the kit only costs £6 after a successful Kickstarter project.