As well you should, as nucleophilicity depends on many external factors, including solvent and type of reaction! But generally, there are four factors you should consider: 1) charge 2) electronegativity 3) solvent and 4) sterics. So (1) charge. Nucleophilicity is basically the measure of a species' ability to donate an electron pair to another species. This is therefore a
kinetic phenomenon. The more isolated and concentrated that charge, the better. So in (A), that negative charge on the oxygen is delocalized in the carboxylate and thus is not concentrated on any one atom. Therefore, the nucleophilicity should be low compared to something that has concentrated charge, like methoxide. But nucleophilicity is relative, so we can't say much just from looking at (A).
Looking at (B), this looks better because the negative charge is located on the oxygen and isn't very delocalized at all. So it's quite concentrated there and we would expect (B) to be a better nucleophile than (A). Now let's go on to (C). (C) has the lone pair on nitrogen. So here's where (2) electronegativity comes in. Oxygen is more electronegative than nitrogen. In other words, oxygen holds onto its lone pair more tightly than nitrogen and therefore is less likely to
donate it away. Therefore, nitrogen is more nucleophilic. Note that we can make this side-by-side comparison
only because both the nitrogen and the oxygen have a negative charge. If the nitrogen was tertiary and had no charge, it would be harder to tell, although having charge is usually more important than electronegativity. So (C) is more nucleophilic than (B).
Okay, so we arrive at (D). Now (D) is very similar to (B), except that it has a CF3 group attached to the alpha carbon. We know that fluorines are incredibly electron-withdrawing due to their electronegativity and therefore the CF3 group is very electron-withdrawing. Therefore, we would expect charge density to go towards the trifluoromethyl group, thereby decreasing charge on the oxygen. As we said earlier, concentration of charge is very important for nucleophilicity. Therefore, we would expect (D) to be less nucleophilic than (B).
So now let's fit all of this together like a logic puzzle. B is more nucleophilic than A and C is more nucleophilic than B. D is less nucleophilic than B. Putting it all together, here are the species ranked in order of decreasing nucleophilicity. C > B > A. We know that D is less nucleophilic than B, but we need to know its position relative to A. So we said that A is not nucleophilic because of resonance delocalization and D is not nucleophilic because of the inductive effect. Generally, resonance is a more effective delocalizer than the inductive effect so from that, we can say that A is the least nucleophilic because the charge is less concentrated on the oxygen.
Notice that we haven't touched upon factors (3) or (4). These will change depending on your solvent and reaction. So for instance, a polar protic solvent will tend to H-bond with nucleophiles and thus reduce their nucleophilicity by tying up their lone pair(s) in H-bonding. Sterics also affect nucleophilicity because like we said earlier, nucleophilicity is a
kinetic effect. So imagine a nucleophile attacking an electrophile. If that nucleophile is really bulky (imagine
t-butoxide), then it'll have a hard time getting near the electrophile. So we would say that it's not very nucleophilic.
For an in-depth analysis of nucleophilicity, see:
http://www.masterorganicchemistry.com/2012/06/18/what-makes-a-good-nucleophile/
