Kester 44 63/37 is the only solder I really use now... the quality of Kester in general is fantastic and the 63/37 is a pleasure to work with.
Kester has other really interesting stuff too, like the 245 and 275 No Clean, but for 90% of us, good ole Rosin core 44 will do just fine. Rosin from what I understand is the most aggressive cleaning flux anyways which is really good for stuff we do. Some of the other fomulas are better for clean, brand new parts you would probably find in a production environment, but I do like the no clean portion of it. The joints come out looking like professionally manufactured PCBs without any of that weird colored flux pool.
Edit:
(with 60/40 if you are holding the wire trying to solder it and its moving as it cools, you can keep moving it as it start to solidify, too much movement and you get what starts to look like a cold joint. With 63/37 that transition from fluid to solid is about near instant. The second it crosses that temperature threshold it just goes solid and holds in place.) Kinda hard to explain, but I still have plenty of 60/40 left and every time I use it, it becomes more and more apparent. 60/40 seems to glob more, where 37/37 feels thinner and seems to flow better. Wire joint look a bit cleaner, but for through hole its harder to tell.