Just off the top of my head...
Before Tom Benson took over the ownership of the team, there was extensive flirtation with moving the team to Jacksonville. And I don't know if you were called it a "failed" relocation considering the circumstances, but there was the possibility of the Saints simply staying in San Antonio after Hurricane Katrina.
For the Spurs, before moving into the Alamodome and in that awfully dark post-Gervin/pre-Robinson period, the Spurs were potentially moving to either Minnesota or New Orleans.
Speaking of San Antonio, Red McCombs also did a prolonged song-and-dance with the Vikings potentially moving to the Alamo City, even doing preseason games to "gauge interest".
And back to Minnesota, there was an effort to move the Minnesota Timberwolves to New Orleans in 1994, just four years into their debut, with the names New Orleans Rhythm and New Orleans Angels being thrown around. However, the bid was rejected due to questions about where Top Rank, the investment group that sought to move the team, was actually getting their money.
Also for the Sacramento Kings, remember the Maloof Brothers were eyeballing Las Vegas and even Virginia Beach.
There's of course the now legendary overnight move committed by the Colts moving from Baltimore to Indianapolis, but remember that if it wasn't for Jim Irsay Sr. being a belligerent drunk, the Colts had an initial deal with Phoenix but the city backed out due to the perceived backlash.
There's the infamous move by the Seattle Seahawks in 1996 where they announced they were moving to Los Angeles (well, Anaheim specifically)...before actually informing the league about it. If I recall, they were even drawing up a new identity.
And I think just about any MLB team in the seventies and eighties used Tampa Bay as a threat, with I believe the Giants going as far as actually making caps with "TB" on it.