Just about any IC can be replaced using the right tools, so it is certainly possible.
However, as Dave says a hot air tool is required at the minimum, plus some solder paste and preferably a proper syringe/stencil to apply to pads when fixing new IC (or tin the pads using normal solder can work)
Something like below is an example of a cheap rework station with both hot air gun and temperature controlled soldering iron:
We have a couple of these here and although only ~£100, this model holds up well in comparison with more expensive options. Both hot air gun and iron work very well for most SMD work, and the iron is compatible with Hakko tips/elements which makes replacements easy. There are cheaper hot air only options available on eBay, have a browse around.
Anyway, that's the kind of thing you need. Unfortunately replacing motherboard RAM of the type shown in the linked pictures is not the ideal first project.
When using hot air on densely populated boards, it's easy to end up removing more components than you intended to. The correct nozzle needs to be used to direct the air stream, and also the surrounding and underside components need to be heat sinked/shielded (e.g. aluminium foil) to prevent this happening.
Another thing to note is that if the problem is a faulty joint, it's possible you can fix the existing RAM by just reflowing the connections, so I would try this before actually attempting replacement if going ahead. I have heard tales of folk putting their motherboards in the oven to do this (with plenty of Al foil to protect the delicate parts) but it's obviously more of a lottery to do it this way.
3Removing chips from the motherboard without damaging it will require a hot-air tool at a minimum; preferably a full rework station with preheader. – None – 2012-09-16T20:21:18.073