Following on from Matias' post, here's an example of an annoying problem faced by lab people, and a cool way to fix it.
The process of stitching together various bits of DNA to make plasmids for use in experiments occupies a large amount of time for many molecular biologists, especially in the early stages of a project. The most established way to do this is to use restriction enzymes and ligases in vitro to chop DNA up and stick it back together, and then stuff it into bacteria to select intact plasmids and amplify them. The fidelity of the process is generally good, but mutations do arise sometimes. I just found one such mutation in my plasmid - four base pairs of a critical recombinase recognition sequence deleted. Worse, this mutation is also present in the lab stock of the parent plasmid. Now here's the big difficulty in using restriction enzymes - they cut at a defined sequence, and if you need to modify part of the plasmid without convenient restriction sites (like this one), you're stuffed.
Or perhaps not. Recently (at least more recently than restriction enzymes) a new set of methods dubbed 'recombineering' have been developed. These take advantage of the fact that homologous recombination can occur in bacteria. So if you make a construct with some homology either side of the region you need to fix, and with a correct version in the middle, you can introduce this into the bacteria carrying the mutant plasmid and get replacement of the broken bit. I took advantage of the fact I was fixing a Cre recombinase site (lox site) and replaced the broken site with an antibiotic resistance gene (bsd) flanked by two working lox sites - meaning I can select for the replacement first, then use Cre to delete the marker and restore a single, functional site. Amazingly it actually worked - yay for small victories.
Most lab bacterial strains are recombination defective (recA mutation), to give better plasmid stability, so to use this technique you need to reintroduce the recombination function to the bacteria. Of course this carries the risk of causing other random plasmid mutations (due to recombination between small bits of homologous sequence) - so let's hope I didn't just make things worse :)
Highly technical diagram below - the lox site represented by a triangle. There are a lot of other uses for this technique, more info here http://www.nature.com/nrg/journal/v2/n10/abs/nrg1001-769a.html

SJP
Recombineering
Just to add that multiple selection markers can be used to select for different events and to obtain homozygous ES cells. Although small mutations can be introduced into the genome in a single step, without a positive selection marker, for instance using a replacement vector.
recA
This is a stupid question, but do you / can you get rid ofrecA once you've done the fix?
Yes
Yes - the most common method is to have the recombination genes (they're actually the genes from phage lambda which control integration etc) under the control of a heat-inducible promoter. So you give the cells a short period at 42C just before you electroporate your DNA, and return them to 32C afterwards, which should minimise the period in which the bugs are recombination-competent.
As the plasmids I use are multiple copy, I usually find that recombination doesn't occur on all of them - only one correctly recombined plasmid is required to provide the antibiotic resistance - so you get some intact plasmid left over in the cells which can still replicate, giving you a mixed population of plasmids. So you need to prepare DNA and transform it again into a normal recombination-deficient strain. The uptake of plasmid is a comparitively rare event, so each cell probably only receives one plasmid molecule which then replicates, giving you recA- bacteria carrying pure plasmid populations.
Piggy, I'm talking about bacteria and plasmids, not ES cells. I have heard that recombineering can be efficient enough not to need selection, but I hope I never need to do that! Ditto and doubled for engineering ES cells without selection...sounds like a proper nightmare to me.