My money would be on Tal. But yeah, strictly guessing.
Longest Unbeaten streak?

Misha Tal, 95 games between October 23, 1973 and October 16, 1974.
Second best, Tal again (84 games).

Games played is definitely the best measuring stick. People always cite Capablanca's 8 year period of 'invincibility', but he didn't actually play as many games as Tal's 1 year span of domination.

Wow. Didn't know Tal was that dominant? Was it weak competition?
Mixed.
A player like Carlsen can't approach such a record, because he does not play in Open tournaments, and his competition is always top notch.
Might be mildly off-topic, but The Life and Games of Mikhail Tal (written by Tal himself) is the most enjoyable chess book I've ever read. 500 pages of sheer brilliant love for chess, deep analysis and vibrant stories from tournament circuits and top matches. I should buy a new copy, my old one is literally coming apart :P

In terms of games played, it would be Tal with 95 games (46 wins, 49 draws) from October 23, 1973 to October 16, 1974. He also has the second longest streak of 84 games (47 wins, 39 draws) from July 1972 to April 1973.
In terms of time, Capablanca was undefeated for 63 games (40 wins, 23 draws from February 10, 1916 to March 21, 1924.
Source: Wikipedia

It's funny how Tal has the longest unbeaten streak, since he probably took more risks than any other player.

I thought Kramnik and Wang Yue both broke Tal's record. But the Chinese GM's record was done playing considerably lower levels of competition.

It's funny how Tal has the longest unbeaten streak, since he probably took more risks than any other player.
If anything, it just shows how he really is the Magician of Riga. He played the riskiest, most double-edged style possible, and he made it work like no one ever did, or has since. Truly a testament to his strength.

I thought Kramnik and Wang Yue both broke Tal's record. But the Chinese GM's record was done playing considerably lower levels of competition.
Ummm... probably the other Wang Hao, the table tennis champion?
He was world's #1 for some 20 consecutive months.

The thing about Tal's unbeaten streak is that he was able to change his style as he got older. He took fewer risks in the 1970s than in the 1960s. As a result, he didn't win quite as many games but he also didn't lose as many.

I found an article in the NY Times that discusses Wang Yue's (82) and Kramnik's(82) streaks along with Drasko's (84) unbeaten streak. But Wang Yue and Drasko didn't consistently play as many elite GMs as Kramnik did during his streak. The author isn't sure, but gives credit to Mikhail Tal(93 and 86) for having the longest unbeaten streak.
http://www.nytimes.com/2008/12/21/crosswords/chess/21chess.html?_r=0
In terms of games played. Does anyone have any idea? Probably Kasparov?
Not including blitz or rapid games.
Magnus is currently at 34 i think.