It sounds like your technique is wrong. You should never put the solder to the iron (except to wet the iron), so you should never be in a position to have blobs of solder on the iron. Put the iron to the two parts to be soldered, then touch the solder wire to the parts (not the iron). Once the solder flows it should coat the two parts. Remove the iron and it should be a good solder joint. Wipe the extra solder off on a wet sponge or solder cleaning wire coil. Then apply a bit of solder to rewet the iron before putting it away.
Also, my guess is you need a better iron. I had one of those low powered non adjustable irons and it was very difficult to use since it couldn't heat up the wires and components fast enough. I replaced it with an adjustable Weller and then a thermostatically controlled Hakko. Both were a vast improvement, but the Hakko is really nice and well worth the bucks if you are going to solder frequently.
I think the advice contained in this thread is good. However I just thought of something nobody has mentioned. Occasionally in repairs, you will come across a component that was made using aluminum or steel wire. Both of these require special processes and are difficult or almost impossible to re-solder using normal rosin core solder. There are special fluxes for aluminum ( at high temperature, I think ), and steel I believe is soldered with silver. These materials can look like they have been soldered normally, but actually a special process was used at the factory.
My guess is that you are NOT running into this, but it is a possible explanation when you run across a wire that simply will not solder normally.
Also not mentioned, but I have no idea if it matters or not, is the "new formulation" for solder to meet the lead-free initiatives. Personally, I do so little soldering so my spool of 1960's era 60/40 solder will probably last for the next 3 generations.
In the past the new alloys were characterized as being more difficult to handle than Sn40 alloys.
So far I have not used the new ones.
What are your experinces with them?