How did the original/classic Doctor Who end?

How did the show originally end? Was it known at the time this would be the final series or did it just 'stop'?

The show was cancelled at some point during production of Series 26, which aired at the end of 1989. It was too late at that point to come up with a proper ending, plus there was an expectation among the cast and crew that the show would be revived at some point, so script editor Andrew Cartmel merely inserted a brief monologue to go at the very end of the final episode, implying that the Doctor's adventures would simply continue forever:

DOCTOR: There are worlds out there where the sky is burning, the sea's asleep, and the rivers dream. People made of smoke, and cities made of song. Somewhere there's danger, somewhere there’s injustice, and somewhere else the tea's getting cold. Come on, Ace — we’ve got work to do!

Following this, an attempt was made at reviving the series for American audiences in 1996. A TV movie was created as a backdoor pilot, but its ratings in the US were disappointingly low, and the pilot wasn't picked up for a full series. The pilot is canon, and continues where the classic series left off, but does not bridge the gap between it and the modern series.

The Ecclestone series did not, as far as I recall, make any direct reference to The Doctor's regeneration as Ecclestone. Do we even know there are not additional regenerations in-between the old and new shows?

The Doctor is known to have regenerated three times between the end of the classic series and the start of the new one:

• The TV movie mentioned above begins with the Seventh Doctor (Sylvester McCoy; the same Doctor from Series 26) being shot, dying in an Earth operating theater, and regenerating into the Eighth Doctor (Paul McGann)
• The minisode "The Night of the Doctor", a prequel to the 50th anniversary special "The Day of the Doctor", depicts the Eighth Doctor dying in a spaceship crash during the events of the Time War, and regenerating into the War Doctor (John Hurt)
• At the end of "The Day of the Doctor", the War Doctor hobbles into his TARDIS and begins to regenerate into the Ninth Doctor (Eccleston)