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Bruce Willis and Demi Moore's eldest daughter, Rumer Willis, showed off her A-list genetics by flashing her smokin' hot bod in a black bikini in Cancun this weekend.

Another member of Hollywood royalty has gone two pieces.

A week after free falling from 24 miles up in the air and breaking the speed of sound, hunky daredevil Felix Baumgartner traded his space suit for hip downtown gear and hit up trendy NYC hotspot Sons of Essex on Monday.

Wearing similar his and hers aviator sunglasses, A-Rod and Torrie looked like ever the happy couple after having lunch and shopping together.

If you recall, Alex allegedly hit on the ladies -- with the help of a bat boy -- during the American League playoffs by having them write down their phone number on a baseball.

Eva Longoria has a nasty red blotch on the back of her neck -- and she's probably THRILLED about it ... 'cause it used to be a tattoo of her ex-husband's basketball jersey number.

Back in January, Longoria began laser treatments to erase 3 Tony Parker-inspired tats -- the "NINE" tattoo ... the wedding date tattoo on her wrist ... and Tony's initials (which were put on a very private, undisclosed location).

Tattoo removal doesn't happen overnight -- it takes multiple sessions, which have to be spaced out over several months.

Lance Armstrong has GIVEN UP on Nike ... after Nike gave up on him ... 'cause the disgraced athlete was sportin' a pair of ASICS while jogging in Texas this weekend.

As we previously reported, Armstrong was dropped by nearly all of his sponsors last week ... in the wake of a report by the U.S. Anti-Doping Agency in which Armstrong is accused of being one of the worst cheaters in the history of sport.

In addition to being banned from cycling for life, Armstrong was also stripped of his 7 Tour de France titles early Monday morning.

Plus, several major Livestrong donors are calling for their money back ... claiming they were duped into donating to the charity "based on a fraud."

Despite the criticism, Armstrong -- who stepped down from his role as president of Livestrong because of the scandal -- wore his yellow bracelet on his wrist this weekend.

Sporting his new wedding ring, Justin Timberlake was spotted out in Fasano, Italy this morning ... after tying the knot with Jessica Biel yesterday.

Some of the famous peeps in attendance reportedly included JT's pals Andy Samberg and Timbaland, as well as Jessica's former "7th Heaven" co-star Beverly Mitchell.

The couple had been engaged since December after splitting for a brief time in 2011.

In their opening statements, lawyers for Lynne Spears and the conservatorship told the jury ... Sam tried to look like a savior to Britney and would stoop so low as to emotionally torture her.

While lawyers, jurors and reporters hear all about the meltdown of Britney Spears and who's responsible for her drug-fueled downward spiral, Britney was enjoying a frothy drink at Starbucks in Encino.

Check out her boots ... and her bangs.

Britney will not have to take the oath, because the judge in the defamation case has ruled she does not have to testify since she's currently under a conservatorship.

Britney Spears took a huge amount of amphetamines the night she was strapped to a stretcher and placed on a 5150 hold -- so claims Sam Lutfi's lawyer in the opening statements of his defamation case.

Lutfi's lawyer, Joseph Schleimer, told the jury, on January 28, 2008, Britney had an amphetamine script filled. Schleimer says she took 6 to 8 pills early in the day, and several more later and went off the rails.

Lutfi's lawyer also said he tried to get Britney to meet with a psychiatrist 2 days before she was 5150'd, but Brit refused.

And there's this ... during Britney's disastrous appearance on the MTV Awards in 2007, Lutfi felt she was such a mess she shouldn't do it, because she was overweight and didn't rehearse, but Britney wouldn't hear it.

Britney Spears was super-paranoid that her hair contained traces of the hardcore drugs she was using -- and that's why she SHAVED IT ALL OFF during her infamous 2007 meltdown ... at least according to Sam Lutfi.

Sam's lawyer, Joseph Schleimer, has been telling the court ... Britney was a serious drug-abuser ... who had a penchant for crystal meth.

Schleimer suggested Britney was concerned that a judge would test her hair for drugs -- and when it turned up positive, she would lose custody of her kids.

So, Britney ... being Britney ... believed that if she chopped off her hair, she could beat the drug test ... at least that's what Lutfi's lawyer is implying.

Mildred shamelessly brought the book out to a cafe in Bakersfield yesterday -- in full view of a photog who just happened to be there -- where she may have finally learned that the steamiest parts of her affair were CHOPPED from the final version.

Seriously ... when Arnold brings up Mildred in "Recall," he goes from "she worked in the house" right to "when she gave birth to the kid" ... completely blowing off the dirty details of the courtship.

Here's the exact passage:

"Mildred had been working in our household for 5 years and all of the sudden we were alone in the guest house.

When Mildred gave birth the following August, she named the baby Joseph."

Rupert Sanders has proven ... you CAN bang a hot Hollywood actress behind your wife's back and still make it all good again ... and we have the pics to prove it.

Rupert and Liberty Ross shared a great big HUG after leaving a counseling session in Beverly Hills Wednesday. We broke the story ... just weeks after the Kristen Stewart cheating scandal broke, Liberty and Rupert were seeing the counselor.

We also told you ... Liberty went to see a divorce lawyer after the story broke but she has not pulled the trigger and wants to save the marriage.

Our sources say Liberty has laid down some ground rules for any reconciliation ... which includes an extramarital banging ban.

Judging by the hug, it seems they're making some serious progress ... but neither Rupert nor Liberty was wearing a wedding ring at the time of the embrace. They arrived and left separately.

Seems to be the season for forgiveness ... just a few days ago, Robert Pattinson was photographed hangin' out with Kristen.

"90210" star Shannen Doherty HAS A BUN IN THE OVEN -- but it's not the baby kind ... it's the burger kind.

Rumors have been swirling today after a photo of Shannen emerged ... in which her stomach was a little more accentuated than usual.

But the actress says there's DEFINITELY NOT a baby in her belly ... just lunch.

She wrote, "I'm a size 2, not sporting a baby bump. That's simply the hamburger I wolfed down 2 minutes prior."

Shannen's little bundle of joy is expected to be delivered in the next couple of hours.

The new woman in Mel's life is Ashley Cusato ... an actress and stuntwoman who's actually been featured as a stunt double for big stars like Emily Deschanel and Denise Richards.

Sources close to the actor tell us ... the two have been dating for about a month -- and things are going so well, Mel has already introduced her to several members of his family.

In fact, sources close to la familia Gibson tell us ... they LOVE her and are convinced she's gonna be around for a long, long time.

The judge in Halle Berry's custody case -- in which she is asking for permission to take Nahla to Paris permanently -- is ready to rule, and the decision could come down this week ... TMZ has learned.

Sources connected to the case tell us ... lawyers for both sides have wrapped their case and the judge has been noodling over his decision.

Sources say the judge has told both sides, he does NOT want to send them a written decision. He wants both sides to appear in court so he can tell them all at once what he's decided.

Halle, we're told, is frustrated because she wants to get on with her life, but it looks like she won't have a long wait. Our sources say the decision could come down Friday -- IF the judge can get everyone together.

Rob and Kristen were spotted leaving a restaurant with a group of friends Monday afternoon -- never holding hands ... but standing mere feet from each other.

This was the 2nd time in 24 hours they were seen together around L.A. ... just 3 months after Kristen admitted cheating with director Rupert Sanders -- but, even more telling, exactly one month before the release of the last "Twilight" movie. Hmm ...