The only thing worse than pulling weeds is pulling up landscape fabric! My only consolation is that at least we were not the homeowners who had this fabric put in. We inherited it from the previous owners. It is a really bad idea to use landscape fabric, and here is why:
1) It may keep weeds down for the first year or two, but soon it will gather dirt and/or composted mulch (that many people put on top of it) and create a lovely little weed bed.
2) Plants that you want to have grow there don't because they cannot get their roots down deep enough. They starve or dry out, unable to reach nutrients and water.
3) The landscape fabric keeps excess water from draining away.
4) Tree roots sprawl over top and through landscape fabric, making it really hard to dig it up or to plant anything in it.
I cannot think of any situation where I would deliberately use landscape fabric. What is this baneful material? Here's a picture of a small portion of what I pulled out today:

Note it is a plastic mesh, and it is intertwined with roots from every species of growing thing that was ever within 20 feet of it.
If you are cursed with landscape fabric under the flower beds in your yard, all is not lost, it can and should be removed. Here is how to remove landscape fabric:
1) Take a steel pronged rake and scrape away at the top layer of dirt (since some very nice rich soil has probably developed - composted - on top of the fabric since it was put there) or cut away at the sod that has overgrown the edges of the garden, until you find some fabric.
2) Give it a tug. If the top layer is light, it may come out relatively easily. If not, move onto step three.
3) If the fabric tears in your hand and you can't get much out, use a rake or a shovel to remove the dirt/sod/weeds on top of the fabric so you can get at more of it without the weight on top making it tear.
4) You can also use the rake to roll back sections of cloth and tear it out as you go, allowing the compost to go back on the (newly freed) bare topsoil.
5) A quick way to find more corners of fabric to pull on is to yank at the roots of trees or shrubs running through the cloth. Most often, as you pull them up they will bring up part of the fabric with them, giving you something to grab on to and pull, or at least letting you know where to start raking or digging.
Sounds fun, doesn't it? But the rewards will come! Finally plants will be able to grow there. Drainage will be better, and you'll likely even have some nice soil to start with.
If you're worried about weeds, I've been reading up on this (we have had a lot of weeds to deal with here), and there are ways to prevent most of them from ever coming up without harming the plants you desire to have grow. I am currently placing cardboard on top of areas we aren't ready to plant, and will cover this with bark mulch soon (since cardboard is not very aestetically pleasing). If we decide to plant something later, we will be able to dig through the cardboard and plant just fine. Cardboard turns into compost eventually. It is a natural solution, inexpensive, and you don't have to pull it up later! I'd much rather use cardboard than landscape fabric under my mulch.