I read the wiki article on latent heat but its still not clear to me. Lets say I heat some ice up and the temp gradually rises till it hits 0C then it starts melting. In my college notes they have a graph showing the temperature rise over time and when it gets to 0C it stops rising for a short amount of time so theres a straight line on the graph before it starts rising again. They say that flat line is the latent heat.

This is the graph
http://www.biophysics.uwa.edu.au/e_book/images/8cimg1.jpg

Yeah obviously if your just measuring the ice it won't rise about 0C but if you measured the melted water it could measure more than 0C couldn't it? Have I got this wrong? Will even the water around the ice stay at 0C until all the ice is fully melted?

if the water got warmer it would transfer its heat to the remaining ice in the solution

Oh yeah heat diffuses from areas of high temperature to cooler areas. I didn't even think of that thanks. Does this mean that a bucket full of water and ice will always be approximately 0C as long as you keep replacing the melted ice?

A little side question. How cold can things get? If I'm not mistaken heat is just atoms/molecules with a lot of kinetic energy. Conversely cold must be a lack of kinetic energy. Is there a point where the atoms just stop moving/vibrating altogether?

Yep

http://en.wikipedia.org/wiki/Absolute_zero

Basically near-impossible to actually cool something down 0K, but scientists have got to within a couple billionths of a K ..

(K is just centigrade but it starts at absolute zero)

And yes,a bucket of ice/water should stay constant at 0C as long as there's enough ice etc to stop there being thermal gradients ..

Thanks a lot that answers my question and more.

heres a chapter from my physics lecture notes at university about heat and energy. theres a bit about latent heat in there

http://rapidshare.com/files/161824165/Chapter_20.pdf.html