Paired or not paired? Comparing groups after propensity score matching After matching on propensity score, e.g 1:1 matching, you obtain a matched subset of your data.
The built-in functions in the Matching package, as a prominent example, compares groups before matching by use of non-paired t-test but then switches to the paired t-test to compare groups after matching.
Publications, in medical journals at least, obviously fail to report what type of t-test they have chosen. As far as I can tell, I haven't seen a single one using the paired test, which contrasts rather strongly against J Sekhons Matching package.
I "did like the rest" and used a non-paired t-test to compare continuous variables in a propensity score matched cohort (1:1 matched).
Was this wrong?
 A: I personally find results are very similar when you use paired and unpaired tests. Yet, my recommendation, built upon studying quite extensively the topic, and following authoritative sources, such as this one from Austin, is now to use tests that recognize the clustering features of the dataset.
Thus, if I am using propensity score quantiles (eg quintiles), or propensity matched pairs, I routinely use meglm or xtgee in Stata, for continous or categorical variables, and stratified Cox proportional hazard analysis for survival analysis.
Specifically, the following excerpt, also from Austin, is very clear:

When estimating the statistical significance of treatment effects, the
  use of methods that account for the matched nature of the sample is
  recommended (Austin, 2009d, in press-b). Accordingly, McNemar's test
  was used to assess the statistical significance of the risk
  difference. Confidence intervals were constructed using a method
  proposed by Agresti and Min (2004) that accounts for the matched
  nature of the sample. The number needed to treat (NNT) is the
  reciprocal of the absolute risk reduction. The relative risk was
  estimated as the ratio of the probability of 3-year mortality in
  treated participants compared with that of untreated participants in
  the matched sample. Methods described by Agresti and Min were used to
  estimate 95% confidence intervals.
We then estimated the effect of provision of smoking cessation
  counseling on the time to death. Kaplan-Meier survival curves were
  estimated separately for treated and untreated participants in the
  propensity score matched sample. The log-rank test is not appropriate
  for comparing the Kaplan-Meier survival curves between treatment
  groups because the test assumes two independent samples (Harrington,
  2005; Klein & Moeschberger, 1997). However, the stratified logrank
  test is appropriate for matched pairs data (Klein & Moeschberger,
  1997).
Finally, we used a Cox proportional hazards model to regress survival
  time on an indicator variable denoting treatment status (smoking
  cessation counseling vs. no counseling). As the propensity score
  matched sample does not consist of independent observations, we used a
  marginal survival model with robust standard errors (Lin & Wei, 1989).
  An alternative to the use of a marginal model with robust variance
  estimation would be to fit a Cox proportional hazards model that
  stratified on the matched pairs (Cummings, McKnight, & Greenland,
  2003). This approach accounts for the within-pair homogeneity by
  allowing the baseline hazard function to vary across matched sets.

