Lucifer by Mike Carey
Mike Carey's Lucifer series may be the most logical place to head after finishing The Sandman. Lucifer takes place after the events of the Season of Mists arc of The Sandman, and adds another 75 issues to the Sandman mythos.
If you enjoyed The Sandman, you're almost guaranteed to enjoy Lucifer, which contains the same sense of scale and worldbuilding, albeit with more consistent tempo. While The Sandman ebbed and flowed, with some arcs strong and others unfortunately weak, Lucifer manages to maintain a steady momentum until the full weight of the series's events leads to an end on a scale that not even The Sandman could accomplish.
Although Lucifer has recently been adapted as a TV show, the story is quite different, and it's definitely worth reading the comic series instead of, or in addition to, the TV adaptation.
Saga of the Swamp Thing by Alan Moore
On the other hand, while Lucifer is an excellent followup to The Sandman, Alan Moore's Swamp Thing run is the series that The Sandman itself spawned from.
Saga of the Swamp Thing was, at the time it was published, completely revolutionary. While it has certainly aged a bit, it is not hard to see where Neil Gaiman drew his inspirations from while he was working on The Sandman. Alan Moore took over Swamp Thing around 20 issues in and made his entrance dramatic by killing off the majority of Swamp Thing's supporting cast and reinventing the true identity of the titular Swamp Thing.
The Books of Magic by Neil Gaiman
The Books of Magic is another Vertigo-continuity comic. Unlike Lucifer and Swamp Thing, however, The Books of Magic was written by none other than Neil Gaiman himself.
While The Books of Magic draws heavily on lore established in The Sandman, it is worth noting that it draws even more from the world of Alan Moore's Swamp Thing run. Therefore, The Books of Magic may be best read after Swamp Thing, and not before.
The Books of Magic is a short, 4-issue series (although it also spawned a much longer ongoing series, primarily written by John Ney Rieber) which features the character of Tim Hunter, a young English boy who has been given the opportunity to learn magic. By coincidence, he happens to look like Harry Potter, but The Books of Magic predates Harry Potter by many years.
Preacher by Garth Ennis
Unlike the previous comics on this list, Preacher by Garth Ennis takes place in its own world. Preacher has recently been adapted into a TV show, but like the adaptation of Lucifer, this adaptation is not exactly true to the source material. Regardless of whether or not you've watched the Preacher TV show, the Preacher comic series is a definite must-read.
Preacher follows a protestant minister named Jesse Custer as he embarks on a journey with his friends Tulip and Cassidy in an attempt to literally find god. If that sounds overly religious or dramatic in any way, don't let that dissuade you, as Preacher is well known for being filled with somewhat crude humor that sometimes edges on the line of borderline blasphemy.
Saga by Brian K. Vaughan
Saga by Brian K. Vaughan has been summarized before as a sort of mix between Star Wars and Romeo and Juliet, but that description simply doesn't do the comic enough justice.
If you're looking to read a series that's still going on, Saga is one of your best options. With the sheer amount of awards that Saga has been winning recently, it would be no exaggeration to say that Saga is one of the most critically-acclaimed comics currently running.
Saga follows the stories of Alana and Marko, who have married, despite the galactic-level conflict between their races, and their attempts to create a sense of stability for their young, recently-born daughter.