In the US, there are at least three parliamentarians (two Senators and one in the House of Representatives) who are 87 years old. Are there even older people who serve or served in such positions elsewhere in the world? What is the age record for parliamentarian?
I don't know if there are any older cases, but Strom Thurmond stepped down from the US Senate at age 100 years and 29 days, having served just short of 50 years as a Senator for South Carolina.
There are a couple of US Senators who lived longer lives than Thurmond, but neither of them were still serving at 100.
After quite a long career in the House of Commons (UK) as a Labour MP from 1922 to 1924, and 1928 to 1970 (and an arrest for Red Clydeside agitation in 1919 in Glasgow!), he accepted a Life Peerage in 1970, serving in the House of Lords, until he was 101 years old in 1986, when he retired just weeks before his death that same year.
Rita Levi-Montalcini (103)
Scientist, Nobel prize laureate, appointed as Senator for Life in 2001 by the President of the Italian Republic Carlo Azeglio Ciampi. She died in 2012 at the age of 103.
If we're talking about history here, Samuel Young is an example in the UK:
The oldest serving MP whose exact dates are known was Samuel Young (1822–1918) who was MP for East Cavan from 1892 (when aged 70) until his death at the age of 96 years 63 days.2
If you'd rather stick to current members of parliament (though, after re-reading your question again before finally answering, it doesn't appear that you do want to stick to the present--I'll leave this part in anyway as it might be somewhat relevant), Wikipedia has a list of a few older members of the UK Parliament. This list includes Bill Cash--at the time of this writing--the current oldest member of the UK Parliament at the age of 79. So currently there aren't as many older members in the UK at the moment.
Looking at a non-western country, I decided to look at India. It is harder to find the relative ages of all the members of Parliament (at least, in a moderately quick manner), but I was able to track down what I think is the oldest currently serving member of Parliament: Shafiqur Rahman Barq at 90 years old.
As for the oldest person on record, I'm not really sure. Samuel Young (as I mentioned above) is a good candidate at 96. Also, Charles Pelham Villiers seems to tie this record (or maybe Young ties him, since Villiers was first).
Some other potential candidates can probably be in these articles about the Father of the House, the Dean of the House, and the Oldest Member--though I haven't looked thoroughly at them to see if any beat Young and Villiers' record.
From Rajya Sabha, India
The earlier answer about Rishang Keishing was based on an old source, who retired at the age of 93.
From State Legislature
Note: I deleted this answer after there were answers with names of older persons. I have now decided to undelete it. It could serve as a reference.