Note: This was written in August 2015 and has not been updated.
Fielding statistics do not get as much prominence as batting and bowling statistics. Even then, usually the wicketkeeper’s figures are usually given more prominence than that of ordinary fielders.
The present record for catches in the field in an innings is 5 (shared by several, starting with VY Richardson) and in a match it is 8 (where AM Rahane stands alone, followed by several with 7).
Here is a chronological list of all those who have taken 5 catches in an innings:

And a chronological list of all those who have taken 7 or more catches in a match:

VY Richardson had reasonable success at a batsman for Australia in the 1920s and 1930s, including the Bodyline series. He became the first of several to take 5 catches in an innings in his final Test at Durban. He took one catch in the first innings and 5 in the second.
http://www.espncricinfo.com/ci/content/player/7346.html
http://www.espncricinfo.com/ci/engine/match/62637.html
Later generations would know him better as the maternal grandfather of the Chappell brothers. One can see some family resemblance.
When he passed away in 1969, he had seen Ian well set in the Australian team although Greg and Trevor were yet to play for their country.
In 1974, Greg Chappell became the first to take 7 catches in a match. This came in the series which some called “Reverse Bodyline” where Lillee and Thomson swept all before them in a 4-1 win. He took 3 catches in the first innings and 4 in the second.
http://www.espncricinfo.com/ci/engine/match/63137.html
Thus both the records remained within the family until early 1977, when Yajuvendra Singh made his debut.
It had been a traumatic series for India with England winning three Tests in a row, thus sealing the fate of the series before the 4th Test started. India batted first, but YS did not do much, scoring 8 and 15 in the match. He equalled the innings record in the first innings with 5 catches, and added 2 more in the second to equal the record. India won this Test and the final result was an England win at 3-1.
http://www.espncricinfo.com/ci/engine/match/63177.html
After this, the feat of taking 5 in an innings and 7 in a match became common. But Yajurvindra Singh remains the only one to achieve these on his debut, a small consolation for a disappointing 4-Test career though he did well enough in first-class cricket. He was distantly related to Ranjitsinhji and Duleepsinhji.
http://www.espncricinfo.com/ci/content/player/36072.html
We finally move on to the anti-climactic Test at Galle in 2015 where India failed to chase 176-but this was on a ground where the highest winning fourth-innings chase was 99. AM Rahane took 3 catches in the first innings an 5 in the second, thus getting a share in the innings record and becoming the only one to take 8 catches as a fielder in Tests.
http://www.espncricinfo.com/sri-lanka-v-india-2015/engine/match/895773.html
http://www.espncricinfo.com/ci/content/player/277916.html
In all first-class cricket, the record is 7 catches in an innings. There are several with 6 catches:

While the record for a match is 10 by Hammond. Rahane just gets into the top part of the first-class record:
