Non-Anion Gap Metabolic Acidosis - USED CRAP
U Ureteroenterostomy/Ureterosigmoid connection- either because of surgical ureteral sigmoidostomy or a ureterosigmoid fistula as may occur in Crohn's disease
S Small bowel fistula, steroid excess (Addison's disease, iatrongenic)
E Extra chloride (NH4Cl or amino acid chlorides 2 to TPN)
D Diarreha
C Carbonic Anhydrase inhibitors, CaCl ingestion, cholestyramine ingestion
R RTA types I (distal), II, (proximal), and IV (hyporeninemic hypoaldosteronism)
A Adrenal insufficiency (e.g. Addison's disease), Alimentation (hyper-alimentation, including starting TPN), Ammonium Chloride ingestion
P Pancreatic fistula, Parenteral nutrition (TPN), hyperPTH, Post-hypocapnia

The mechanisms of the above items causing a non-anion gap metabolic acidosis are as follows:
Ureteroenterostomy or Ureterosigmoid Connection Recall that urine contains large amounts of chloride. But now instead of losing the chloride in the urine, the chloride is passed into the sigmoid colon. This large amount of chloride is then exchanged in the sigmoid colon for HCO3, which is then lost in the stool (GI loss of HCO3).
Steroid Excess
Excess Chloride

Usually iatrogenic (i.e. from patient begin give a lot of chloride-containing fluids).

Can also be from Ingesting large amounts of chloride (in the form of CaCl or NH4Cl)

A large amount of Cl makes it to the sigmoid colon where it is exchanged for HCO3 which is then excreted by the GI tract (GI loss). For NH4Cl also read entry below for "Parenteral Nutrition (TPN)".
Diarrhea (# 1 cause) In the case of diarrhea, as you get increasing amount of dehydration, excess lactate is produced (because of insufficient oxygen delivery). You might expect to get a metabolic acidosis, but dehydration also causes a contraction alkalosis which can normalize the pH or even drive the pH up causing alkalosis.
Carbonic Anhydrase inhibitors Renal reclaimation and generation of HCO3 depends on carbonic anhydrase. So the carbonic anhydrase inhibitors cause loss of HCO3 in the urine. So, CA-I's interfere with renal tubular function and therefore cause RTA.
Renal Tubular Acidosis (RTA)
Addison's Disease
Pancreatic fistula Bicarbonate-rich fluid excreted into the intestines where it is lost (GI loss of HCO3).
Parenteral nutrition (TPN) There is an additional mechanism by which NH4Cl causes a non-AG metabolic acidosis. It is similar to the mechanism by which TPN causes a non-AG metabolic acidosis. Either the NH4Cl or the amino acids in TPN are meatbolized to HCl which causes a transient non-AG metabolic acidosis. The decreased pH and decreased HCO3 stimulate renal tubular reabsorption and generation of HCO3 (secretion of H+). You only end up with a metabolic acidosis if the addition of acid overrides the ability of the renal tubules to secrete H+ and generate NH3+ for excretion in the urine, usually a short-lived process.
Post-hypocapnia In prolonged hypercapnia renal tubular cells compensate for a prolonged respiratory alkalosis by decreasing reclaimation and generation of HCO3 (which takes 12-24 hrs for full affect). If the respiratory alkalosis resolves rapidly, reclaimation and generation of HCO3 will return to normal over 1-2 days. During this period you can get a (resolving) non-AG metabolic acidosis.

The two main causes for non-anion gap metabolic acidosis are diarrhea and RTA . Most of the time you can distinguish between these two based on the history alone. Another way to think about the differential diagnosis of non-anion gap metabolic acidosis is to ask whether or not there is GI loss or Renal loss of bicarbonate.

If the history does not provide an obvious explanation, you can distinguish between GI vs renal bicarbonate losses by determining the urine anion gap (urine AG = urine Na + urine K - urine Cl), where a positive value indicates renal bicarbonate loss and a largely negative value indicates extra-renal bicarbonate loss.

Why is that? Because if a large amount of HCO3 is lost, a large amount of NH+ is excreted in the urine. So, UCl > UNa + UK and get a positive urine AG when you expect a negative one.