At the very beginning of the first book/movie, Harry made glass disappear in the London Zoo without using a wand. Dobby was able to do such things without wand a because he was a magical creature. I didn't think humans could do such things without a wand. One even needs a wand to apparate.
Yes, wandless magic is possible. A wand isn't what does magic (with rare exceptions) - the wizard does; a wand is merely a focusing tool to enable more precision. Exceptionally gifted wizards can do wandless magic, even as kids.
HP Wikia article on wandless magic has plenty of examples, most of them well referenced, including Harry blowing up his aunt, Tom Riddle doing magic while in the orphanage, Lily Potter doing magic (observed by Severus) before getting a letter from Hogwarts and Harry doing Lumos to find his wand.
Canon explains that 'accidental' magic occurs in relation to strong emotion(s) -- this means a witch or wizard can make magic happen without meaning to and without having a wand to channel the magic through. Here's some examples from canon that help to explain this. In Philosopher's Stone:
- Aunt Petunia cuts Harry's hair practically to the scalp, because she's tired of Harry coming back from the barber's looking like he hadn't gotten a haircut. The next morning, Harry's hair had miraculously grown back to its normal length.
- Aunt Petunia tried to force Harry into an old ugly jumper of Dudley's, but the more she tried to pull it over Harry's head, the smaller the jumper got, until it was the size of a handpuppet.
- Harry inexplicably found himself on top of the roof of his school's kitchen when he was running from Dudley and Dudley's gang, and Harry had no idea how he got up onto the roof.
- The boa constrictor incident, where Harry removed the glass to the snake's habitat.
And to answer your question, which is specifically about the boa constrictor incident, I think Hagrid sums it up nicely:
‘Not a wizard, eh? Never made things happen when you was scared, or angry?’
Harry looked into the fire. Now he came to think about it ... every odd thing that had ever made his aunt and uncle furious with him had happened when he, Harry, had been upset or angry ... chased by Dudley’s gang, he had somehow found himself out of their reach ... dreading going to school with that ridiculous haircut, he’d managed to make it grow back ... and the very last time Dudley had hit him, hadn’t he got his revenge, without even realising he was doing it? Hadn’t he set a boa constrictor on him?
Philsopher's Stone - Page - Bloomsbury - Chapter 47, Keeper of the Keys
Wands are not always necessary for magic. There are already several mentions of this in canon, many documented here: Are there any spells that a wizard/witch can cast without a wand in the Harry Potter universe?
And it must have been common knowledge in the Potterverse. When Harry expresses disbelief that he is a Wizard, Hagrid counters by asking if Harry had ever made anything funny happen when he was scared or angry. Hagrid wouldn't have asked that, had he now known it was possible. In fact, Hagrid's question seems to assume that it's common and happens to all underage wizards, because he was pretty sure he knew the answer.