There seems to be a lot of confusion with understanding high density and low density memory modules. I will try and clear this up a little.
A lot of people can obtain high density memory for a ‘cheap’ cost. These as usually branded as generic or do not have a brand name on them. While they save money on this memory, it may not work with their specific motherboard. A majority of motherboards do not accept high density modules. They usually show or register as half of what they spec out or advertised to be (i.e. bought a 1GB module and it only shows as 512MB), or they don’t work at all. This is common on all size modules. DDR and standard SDRAM included.

First rule, Double sided memory is not always low density modules. High density modules can have 16 chips (8 on each side). 'Standard' RAM chips are organized a DEPTH x 8 Bits. E.g. 32x8, 64x8, etc. That means 8 of the chips make up a 64 bit wide rank (memory bus is 64 bits wide). "Double Sided" is an old term to describe a stick with 16 chips, 8 on each side. And with DEPTH x 8 chips that makes for 2 ranks (or, again in an older style terminology: 2 'banks').

'High Density' chips are DEPTH x 4 bits so it takes 16 to make a 64 bit wide memory rank. And this is why "double sided" is no longer the favored description because when x8 chips are used "Double sided" means "double rank" but with x4 chips it takes both sides and 16 chips to make the ONE, single, rank.

Using a 1GB memory module, the 'High density' memory stick crams the 1GB into ONE RANK by using 16 deeper (twice as deep) x4 bit width chips. And this is how they arrive at the confusing term 'high density'. The chips themselves are no higher in density than the x8 chips but since they are organized as x4 they can cram more 'bytes' into a single rank because 16 chips make up a rank rather than 8, not that it helps make the stick itself any 'higher' in 'density' because you can still only get 16 chips mounted on the thing.

A memory 'slot' is usually designed for 'standard' x8 chips and memory sticks containing 2 ranks. That is how the 'capacity' will be described.
For example, a motherboard that will accept 3GB of memory with 3 slots. Each slot will accept a “double rank” module. Never exceeding 512MB per rank.
Next example, a motherboard that will accept 2GB of memory with 3 slots. This would be tricky and would require reading the owners manual of the system board. Typically on these boards, the first slot will accept a double rank module and the combination of the second and third will accept 2 ranks never exceeding 512MB per rank. I.E.
first slot – double rank module
second slot – single rank
third slot – single rank
or
first slot – double rank
second OR third slot – double rank leaving one of the slots empty.

So, a 1GB 'high density' stick puts 1GB in ONE RANK and a 'standard' (low) density 1GB stick is two 512MB Ranks. Same size, same 'density'. It's the RANK organization that's different.

This still doesn’t mean you cannot use a ‘high density’ module in a motherboard. If the slot will accept a double rank module, never exceeding 512MB per rank, you could still use a 512MB ‘high density’ stick of memory, because it is 512MB in a single rank module.

In conclusion, If you don’t know if your motherboard will accept ‘high density’ modules, buy the more expensive ‘low density’ or what they call ‘100% compatible’ modules. The more money you spent, will give you more assurance and less of a headache later.