There are lots of uses for LMLC VPS (Low Memory Low Cost); simple proxy servers for private use or hosting a series of static websites being some of the most popular. For example, I use a Candian VPS to experience browsing as a Canadian might, whilst I have websites running on 64Mb instances that are very unlikely to need any more resource (static sites).
Out of the box, these days, a standard LAMP server will test a 512Mb VPS instance, but there's no reason - if you're not using memory hungry toolchains - that you can't get by with a 128Mb instace - in fact, they are probably my favourite!
So, here's a roundup of low cost, low memory VPS (updated mid 2014).
Tiny OpenVZ Based VPS Services For Clueful Clients
This is actually a spin-off/sister company of RAM Host, which is a fairly respectable player in the budget VPS world (think $5 per month). However, this TinyVZ brand offers 128Mb RAM (dedicated) OpenVZ at $15 per year or KVM at $35.
Even if looks a little bit too much like prgmr to be coincidence, it's definitely worth a look. You won't mind much in the way of a control panel here, so you'll need the technical capacity.
We don't assume you are stupid. Since 2005
The original no frills VPS service. You really do know what you need to be doing here, and with a 64Mb slice of the VPS pie costing $48 per year it's not the most cost effective, but it is Xen (so more performant than OpenVZ) and makes you feel like you're using a very well managed service which doesn't over sell their kit.
Secure Dragon LLC. is a strong contender in the online service industry because our staff has the knowledge and experience of the mystical creature we chose to represent us.
These guys are my provider of choice at the moment thanks to their 64Mb OpenVZ instances starting at $9.99 per year. Good, custom control panel and good communication from the team. Highly recommended if you need a quick low memory VPS at low cost.
I've been a long time fan + customer of RamNode, and only recently are they able to make it in to this post with the introduction on a $15 per year 128Mb OpenVZ tier.
Available in 3 US cities + The Netherlands, this is a great option for a low memory, low cost VPS from a reputable provider (they've been around for a while).
Note the link above is an affiliate link
Other Low Memory, Low Cost Providers
There are a handful of other providers out there doing LMLC VPS on a yearly plan. Drop me a note in a comment if you think they are worth checking out. My main critera for curating this list is provider reliability (in terms of has the company been operating for more than 6 months), as it's particularly frustrating to fork out a yearly cost (albeit a small one) to find the provider has disappeared a few months later.