"Feminine hygiene" products: disposable tampons and pads.
According to 
Natural Matters, "in the U.S. alone, 11.3 billion "disposable" menstrual products per year are disposed of in landfill sites. It takes approximately 500 years for one "disposable" menstrual pad to partially biodegrade."
Alternatives
There are 
reusable menstrual products out there, including menstrual cups, reusable pads, and even special "period panties" and menstrual blankets to protect your bedding at night. There are excellent environmental, financial, and personal health arguments for making the switch.
(a) Menstrual cups.If you prefer tampons, consider using a 
menstrual cup. Inserted into your vagina like a tampon, rather than absorbing your menstrual flow, a menstrual cup collects it over a period of hours. You remove the cup, empty and clean it, and reinsert it to continue to collect your flow.
Although they've only become more readily commercially available recently, 
menstrual cups have been around since at least the 1930s.  
Some say earlier! Some popular brands include 
Divacup and the 
Keeper, which produces both 
Moon Cups, made of silicone, and the original 
Keeper, made from natural latex rubber.
(b) Reusable pads.
Some of the most popular brands are GladRags and Lunapads.
There's a wide variety of different pads made by both companies to meet your needs according to where you are in your cycle and how heavy your flow is. Here's the selection of reusable pads from 
Lunapads and here's the one from 
Gladrags.
There are many other manufacturers out there. 
Here's a list of them from Natural choices. If you want "super cute" pads to wear, you can try 
Punkyspads.
If you're crafty and know how to sew, you can also 
make your own. (Here's 
another source for information on sewing your own pads.)
For more information on cloth menstrual pads, check out the 
rather comprehensive information on the subject at 
Natural Choices.
(c) Padded menstrual underpantsLunapanties come in a couple different varieties.
(d) Menstrual sponges Sea pearls are natural, reusable sea sponges.
Arguments for switchingApart from the environmental impact of using disposable feminine hygiene products, which end up in the landfill, there are also 
financial savings for a woman who ceases to purchase these products on a monthly basis. (See 
Lunapads' discussion of this issue, also.)
Some women find the reusable products more comfortable, as well.
Lunapads: 
Why switch?
More information, supportIf you're considering making the change, but you have questions, there are online communities out there that talk in detail about the issues involved in making this transition. Livejournal has several, including one specifically devoted to 
menstrual cups. Lunapads also has an informational guide on their website that 
helps you choose from among their products.