Honestly, One Piece really does not have alot of filler. Not nearly as much as Bleach or Naruto. There are only a few of filler arcs of any real length and even those are only maybe 10 episodes at the longest. Most of One Piece's filler comes as either little single episode stories or they will add a little bit to the middle of a cannon arc and those you would not even know were filler unless someone told you. One Piece also happens to be my favorite long running series. If you check out Fairy Tail and enjoy it, give One Piece a shot. They have a similar feel to them. Good mix of action and comedy. Pretty much take Fairy Tail and swap mages for super powered pirates and you have One Piece. Word of warning though, One Piece does take a bit to get moving and the beginning episodes are pretty average. It gets much, much better. If you get to Arlong Park, that is where it starts to get really good.
Another couple of series you might enjoy are:
Rurouni Kenshin (
http://myanimelist.net/anime/45/Rurouni_Kenshin) It is about a wandering samurai who uses a reverse blade sword (the cutting edge and dull edge are swapped) since he has vowed to never kill again. He befriends a female Kendo master trying to keep her struggling dojo afloat (among other people) and is really just trying to find a peaceful life, but dark secrets and people from his past keep surfacing that will not let him do so.
Very good shounen series that sadly got a bit of a raw deal when it was made into an anime. The first two seasons range from good to great, but then they did a filler season to let the manga finish. Except the filler was so bad the series got cancelled before they could do the last arc from the manga. It is still very much worth watching and they did animate the finale to the series. There is also a really good OVA that deals with Kenshin's history that is quite a bit more serious and gritty then the series.
The other series is:
Yu Yu Hakusho (
http://myanimelist.net/anime/392/Yu_Yu_Hakusho) This is another shounen series about a kid who is a trouble maker who gets killed sacrificing himself to save young child. This action earns him the change to earn back his life by working as a spirit detective that hunts down and returns troublesome demons to the afterlife. This is really just the starting point for the series.
Very good fights in this series. It also isn't too long at 112 episodes and unlike most shounen tells the whole story with a real ending in those episodes. It is a little bit older of a series from the early 90's so the animation might look a bit dated at first, but I hardly noticed it after an episode or two.
---------- Post added 2011-10-31 at 02:04 PM ----------
Well you have likely seen all the romance, drama, harem series that I have so all I have is a comedy and a couple of cute girl slice of life series.
First up is the one I mentioned to you already:
Soredemo Machi wa Mawatteiru (
http://myanimelist.net/anime/8726/So..._wa_Mawatteiru) very funny series about a clumsy but well meaning girl, Hotori, and a few of her friends who work at a rundown and pretty slow maid cafe and the nonsense they get into. Hototi is voiced by Chiaki Omigawa who I know some people dont like but I think she has a very distinct voice that works really well for Hotori. She is probably best known as Maka in Soul Eater.
Next is
Ichigo Mashimaro (
http://myanimelist.net/anime/488/Ichigo_Mashimaro) Pretty standard cute-girls-doing-cute-things series. One of my favorites of the genre though largely due to the older sister character who is supposed to be watching out for the girls but is just as irresponsible as the younger girls and the totally crazy next door neighbor girl who loves to blurt out random things and usually gets laid out face first on the floor for her troubles.
Finally is
Hidamari Sketch (
http://myanimelist.net/anime/1852/Hidamari_Sketch) Slice of Life that follows the day to day lives of 4 girls who all go to the same art school and live in the same dorms. One of my favorite feel good series. What sets this series apart from the other many high school girl slice of life comedies? One Word. SHAFT. Yup. This series is made by the same studio that did the likes of Bakemonogatari, Mahou Shoujo Madoka Magica, and Sayonara Zetsubou Sensei. It brings that same unique look and style to the slice of life genre. Really great series I think. 3 seasons thus far with a 4th coming soon.