Bottom line:  There is evidence that associates capnography with improved detection of respiratory depression during procedural sedation and in management of mechanical ventilation.

Monitoring during moderate sedation:

PubMed search: (capnography OR end tidal carbon dioxide) AND sedation AND (emergency department OR intensive care OR critical care) AND humans[mesh]
Includes prospective studies, a systematic review and some lower quality comparative studies.

Higher quality study (Randomized controlled trial and prospective studies)
Proehl J, et al. J Emerg Nurs. 2011 Nov;37(6):533-6. Emergency Nursing Resource: the use of capnography during procedural sedation/analgesia in the emergency department.
Systematic review describes evidence from research studies, meta-analyses, systematic
reviews, and existing guidelines. Rates evidence using Appraisal of Guidelines Research & Evaluation methodology.

Deitch K, et al. Ann Emerg Med. 2010 Mar;55(3):258-64. Does end tidal CO2 monitoring during emergency department procedural sedation and analgesia with propofol decrease the incidence of hypoxic events? A randomized, controlled trial.
Patients (n=132) in the ED who received propofol sedation received standard monitoring plus capnography and were randomized so that physicians administering care either had access to capnography readings or were blinded to capnography readings.  RESULTS:  Hypoxia was observed in 17 of 68 (25%) subjects with capnography and 27 of 64 (42%) with blinded capnography (P=.035; difference 17%; 95% confidence interval 1.3% to 33%).  Capnography identified all cases of hypoxia before onset (sensitivity 100%; specificity 64%), with the median time from capnographic evidence of respiratory depression to hypoxia 60 seconds (range 5 to 240 seconds)

Burton JH, et al. Acad Emerg Med. 2006 May;13(5):500-4. Does end-tidal carbon dioxide monitoring detect respiratory events prior to current sedation monitoring practices?
60 patients (enrollment stopped after review of 20 acute respiratory events) underwent capnographic monitoring while under procedural sedation. Abnormal end tidal CO2 findings were documented in 36 patients (60%). Abnormal ETCO2 findings were documented before changes in SpO2 or clinically observed hypoventilation in 14 patients (70%) with acute respiratory events.

Monitoring during mechanical ventilation

PubMed:  (capnography OR end tidal carbon dioxide) AND mechanical ventilation AND (emergency department OR intensive care OR critical care) AND humans[mesh]
Filters:  Systematic reviews

Walsh BK, Crotwell DN, Restrepo RD. Capnography/Capnometry during mechanical ventilation: 2011.  Respir Care. 2011 Apr;56(4):503-9.
Applied GRADE criteria to 200+ identified studies and guidelines. Includes several recommendations for use of capnography in monitoring patients on mechanical ventilation.