I suppose it turns on what you mean as a mystery series. The traditional Agatha Christie type mystery is not really done anymore. Although there are plenty of modern authors with continuing series with private eyes or police officers who solves mysteries although the books are characterized more as mystery/suspense.
Some suggested authors, not listed in any particular order:
David Baldacci. Prolific writer has written a bunch of one-offs but has three good series.
1) The Camel Club series, about an ex CIA type professional killer, going now by the pseudonym, Oliver Stone, who retired from the game and lives in Washington DC and his occupation is just maintaining a graveyard. Has a small circle of friends (call themselves The Camel Club) who get involved in government intrigue plus issues from Stone's past.
2) Sean King/Michele Maxwell series. Two ex-Secret Service agents who now run their own private investigation firm. Just re-read their first pairing called Split Second and it, along with 2-3 subsequent books are really good.
3) Will Robie series. A government paid hit man for enemies of the state. Has three books that are pretty good.
Michael Connelly - The Harry Bosch series. About a 20+ book series dating from the 80's to the present about an LAPD detective.
Jeffery Deaver - The Lincoln Rhymes series. Rhymes is a quadriplegic forensic expert who solves crimes as a consultant to the NYPD with his protégée Amanda Sachs. Deaver probably reminds me the most of Agatha Christie of any contemporary author as there is a lot of misdirection in his books. The first in the Rhymes series, The Bone Collector, was made into a movie some years back with Denzel Washington.
Sue Grafton - The Kinsey Mulhone series. Started in 1982, one of the first series featuring a female P.I. Each book, starting with A is for Alibi, represents a letter of the alphabet and she is now up to W. One of the first P.I's with foibles, and while a good series, Grafton ran out of steam around the letter M and I haven't much cared for the books after that.
Sara Paretsky - the V.I. Warshawski series. Another female P.I., based in Chicago, started about the same time as Grafton although the series never had the drop off in quality in recent years that has plagued the Mulhone books. An entertaining and well crafted series.
Ian Rankin. - The John Rebus series. This is about a Scottish police inspector who is not a real likeable character, a bit of a drunk, insubordinate to his superiors and tends to bend the rules. I really like this series but several people I have recommended it to found the Rebus character leaves them cold.
Finally, if you want a traditional Agatha Christie type mystery, check out her contemporary Erle Stanley Gardner, whose books you can get real cheap on EBAY or in any used book store. You are obviously familiar with his Perry Mason character from the TV series, but the Mason books are well plotted mysteries with no wasted pages on subplots involving the characters or their relationships outside of the law office. Best of the Mason series were written in the 50's (I would avoid anything written before that). Actually a better series, for me are the books featuring the Bertha Cool/Donald Lamb detective agency, which the characters seem more human, and with some surprising humor. Also Donald Lamb is free to do some illegal/unethical things that Gardner could not have Mason do (being an attorney)
I could list some other authors, but the above should suffice for starters.
