Vacuum cleaner
Filter Types
Cloth Bag
A cloth filter eliminates the cost of bags, and is less likely to clog than paper.
The bag must be emptied, which can be messy.
Performance is middling.
Old cloth filters generally need a thorough clean to restore full suction power.
Paper bag
The bag is disposable, making emptying more or less mess free.
A new paper bag every time means ongoing expense
Paper filters clog very rapidly on building dust.
Cyclone
Cyclones are good for building dust
Some cyclones have additional filters that must be replaced from time to time.
Cyclone vacs with no other filter lose no suction at all due to the filter. In contrast, the back pressure produced by paper & cloth bags is significant, and worsens considerably as the pores clog.
This is partly but not 100% true for cyclones with additional cloth filters, as those filters will give some airflow resistance that increases over time. The presence of the cyclone filter means that much less clogging occurs, but they will still clog eventually.
Dysons have gained a poor reputation for reliability as well as price. Other makes don't generally seem to suffer the same frequent problems.
DIY Cyclone
DIY cyclone filters are easy to make, and can be added to any existing hoover or air filtration system.
http://www.internode.co.uk/cyclone/
http://www.woodcraft.com/articles.aspx?articleid=408
Water
These uncommon vacs use a tub of water to trap the dust.
Presumably the water needs emptying after each use.
Reviews
Earlex & DIY cyclone on uk.d-i-y