Solder types?

[mariush]

If the above link isn't good enough, this should also help: http://en.wikipedia.org/wiki/Solder#Solder_alloys

You can choose between two kinds of solders : eutectic solders or not eutectic solders. 60/37 is just one alloy that's eutectic, it becomes solid or liquid at exactly 183c.
Eutectic solders transition from liquid to solid in a very small range of temperatures, some under 1 degree Celsius.  The other types of solder have a certain region in which they're plastic, they're between solid and liquid. For example the classic 60/40 has a region between 183 and 188-190 degrees Celsius.

Eutectic solders are better for situations where there's vibrations or you want to control very well how fast the connection hardens and joint is made.
Non-Eutectic solders are good for situations where you want to take advantage of that plastic region of the solder, for example if you'd want to desolder a connector or something else you may want to add some of that solder and heat up every solder point and extract the part as the solder on each connection point is still in the semi-liquid state.

Then there's solders that contain Lead and solders that don't contain lead.  Solders without lead usually melt at higher temperatures, usually 217 degrees Celsius or more, so it's more difficult to solder because your iron has to be hotter which in turn can shorten the life of the iron tip (hotter iron tip means more oxidation, means less iron tip life).
Also, it's more difficult to desolder or solder componetns on commercial products such as motherboards because these products typically have a lot of copper in the pcb layers which sucks all the heat from your iron tip, thus you iron can't reach that 217c+ temperature easily.

If you solder at home, hobby stuff, there's no reason not to use leaded solder, unless a particular component is tinned with a material that would react negatively with your solder (it's very rare).
With lead free solder, it's often best to use solder that works best with particular components, for example some surface mount components are tinned with silver, so it would be a plus to use solder that has a tiny bit of silver in it.
Other people use solder that has a bit of copper (Cu) in it, because this type of solder is easy on the iron tip, it lasts longer in theory. But an iron tip is generally cheap and lasts a long time, so you shouldn't select a solder wire just on this reason alone.

One reason lots of people are afraid of leaded solder is all the misconception about lead being toxic and so on. The reality is lead used in the solder doesn't get heated up to such degree by the solder iron that it would turn into vapors or particules going into your body, so you won't "absorb" lead by soldering using leaded solder. The only way you would get lead from soldering with leaded solder would be from rubbing the solder wire in your hands for hours and even then, it would be a minuscule amount of lead particles - you probably breathe more lead daily than what you'd absorb that way.

In fact, it's actually worse for you to solder using lead free solder.

All solder wires have flux built in - flux is a sort of acid that is solid inside the wire (in a somewhat neutral state) but turns to liquid (and acid) when it warms up from the iron tip and pours over the surface you want to solder, attacking the oxides and preparing everything for the actual solder. This way, a good connection is made.
In a lead based solder, flux typically melts at around 160-180c and has a bit of time to "attack" the surface before it evaporates from the heat of your iron tip.

As lead free solder turns liquid at higher temperatures, people need to use irons at higher temperatures and manufacturers also have to use more powerful/corrosive fluxes that would attack the surface much faster because the flux will be burnt or will evaporate much faster due to the higher iron tip temperatures.

The smoke from all fluxes is bad for your lungs but lead free fluxes are generally much worse than the mild fluxes used in leaded solders.

So if you're not educated, you may think you don't get lead poison by using lead free solder, but you're actually hurting yourself more if you breathe in that smoke coming from the lead free solder.

//ps There is some debate if it's a good idea to combine leaded solder with lead free solder... for example if the pads or holes on a pcb are tinned with lead free solder, some say you should not use leaded solder on the pcb, because the joints will be weakened.  I don't think it's such a big deal in the "grand scheme of things" but you may want to do more research about it.

Beginners that read this thread may want to learn a lot about soldering from this old series made by Pace - even though the videos seem a bit outdated, the information inside is still valid:

[jay]

This discussion thread is going to cost me some money  I've been using 60/40 and now decided to get other types.. A local shop where I'm about to get other things does not have 63/37 but they have Sn62 Pb36 Ag2 and Sn62 Pb37 Cu1. After studying wikipedia and couple of other sources I'm almost sure that those are also eutectic and similar in use. Will I get the 63/37 magic experience also with 62/36/Ag2?

[nanofrog]

Will I get the 63/37 magic experience also with 62/36/Ag2?

Yes. 

It's eutectic like 63/37, and has a slightly lower melting point (179C instead of 183C). Meant to be used on parts/components that are silver or silver plated to prevent leaching, but won't hurt anything that's not (just more expensive due to the silver content).