First, the daily maximum and minimum temperature records: 2013 saw a large number of daily records for both warmth and cold; the total for the year was 32, only slightly behind 1969 and 1992 (33 records each). [Note that here I am looking only at high maximum and low minimum temperatures, not low maxima and high minima.] The long-term temperature trend is evident, with more warm records broken in the last two decades, and far fewer cold records broken since the Pacific climate shift of the mid-1970s. One other interesting feature: only one year (1972) saw no high temperature records, while 8 years saw no low temperature records. So it seems that cold temperature records are slightly more clustered in time.
Next, daily precipitation and snowfall records. There is no obvious trend in the precipitation records, but it seems that fewer snowfall records have been broken since 1976. Note that 5 daily precipitation records have been set so far in 2014, with today's event not quite adding to this count.
Finally, I also looked at the records for monthly mean temperature and monthly total precipitation and snowfall; see the charts below. Again the temperature records are the most interesting, with a cluster of record warm months from 1975-1981 and none prior to 1975. Two monthly temperature records were broken in 2013 (cold April, warm October); 1979 was the only other year with both a record warm month and a record cold month. For snowfall, the period 1991-1995 saw record snowfall for 5 of the 10 months, although the 1995 record was for the only August snowfall in the history (0.1 inches).
In conclusion, 2013 was certainly an extreme year for breaking temperature records, and was a little more extreme than "usual" for precipitation and snowfall; but other years of the past decade do not stand out as especially unusual.
Update July 9: I've added charts below for the daily low maximum records and high minimum records, as well as the total of all four daily temperature record types. 1992 really stands out here for the low maxima, and 2013 tied with 1981 for most high minimum records. In all four categories combined, 2013 was second only to 1992 in terms of the number of temperature records. However, 2013 was very unremarkable in terms of the number of low maximum records.