
The low-cost offers I have seen have the following in common:
One place to look for these providers is at a website called WHT, or at BudgetVPS (who have a special link for plans that cost $2 a month or less).
Some current providers of plans that costs $20 a year or less (prices rounded to the nearest dollar):
"Burst" memory usage is memory that can be allocated, but, if the server as a whole is low on memory, processes may be killed if more memory is being used than one's "normal" memory usage.
An OpenVZ guest doesn't allocate cached and buffer memory; this is only seen on the host. The only memory one sees when typing in free in an OpenVZ guest is memory used by malloc in one's processes. For example:
$ free
             total       used       free     shared    buffers     cached
Mem:        262144      29376     232768          0          0          0
-/+ buffers/cache:      29376     232768
Swap:            0          0          0
This is the output of free on an OpenVZ guest with 128 megabytes of
"normal" memory and another 128 megabytes of "burst" memory.  Compare this 
to free on a native Linux host:
$ free
             total       used       free     shared    buffers     cached
Mem:        511516     489544      21972          0      62204     202884
-/+ buffers/cache:     224456     287060
Swap:      1048568       2476    1046092
Here, we can see buffers being used, as well as cache and swap.
On an OpenVZ guest, memory usage is seen with free, disk usage is seen with df, and network usage can be seen with ifconfig (presumably, the ifconfig number is reset whenever the system is "rebooted", so it may not be an accurate number).
It is amazing how technology has made getting an internet presence very, very affordable.
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Errata: BuyVM does intend to sell ultra-low-cost plans again; this article implied otherwise and has since been corrected.