Hi Jazza & All,
Personally, the record for me is Q 1224-1116, a QSO (Quasar) in Virgo not far from M104. It has a redshift of 1.98 implying a "look-back time" of about 10.8 billion years.
When you observe that quasar, you are looking at light more than twice as old as the solar-system.
There is a (short) list of some brighter quasars here:
http://seds.org/~spider/spider/Misc/qso.html
many of which are visible in moderate-sized amateur 'scopes.
A much more complete list is here:
http://www.klima-luft.de/steinicke/KHQ/khq_e.htm
I seem to remember the most distant object visible in amateur-sized 'scopes is a QSO in Ursa Major at about mag 17 that has a redshift of 3.1 implying a look-back time of about 12 billion years.
As for most distant (ordinary) galaxy, I'm not certain but I think the record holder for me is a galaxy (MCG +5-36-020) in AGC 2065 in Corona Borealis that, assuming the Hubble Constant to be 71 kilometres per second per megaparsec, is about 950 million light-years away.
That observation was made with 31cm (12") back in 2000:
x186 26' TF. Mag 15.1 Size 0.4' This is a very very difficult observation. Found - there is a line of *s in roughly PA 45 from the N mag 12, 13, 13.5 *s from NE-SW. Middle * is displaced to the SWfrom centre. From that * in PA 60, 2.5' distant is a threshold dot only 10" diameter which is very occasionally visible about 4 times in 5 mins of observation. Only very occasionally wafts into view for a couple of seconds, 90% certain. G Mitchell confirms.
I've seen lots of others with 12 & 18" between the 500 and 900 million light-years mark. There may be a few others a little more more distant than this -- I haven't kept any stats on that.
Hope this helps,
Best,
Les D