Misbehaving applications and poorly written code can cause memory leaks. These occur in many operating systems and applications including Linux and Windows.
Microsoft has _plenty_ of technical articles and patches to fix leaks in many different versions of Windows up to and including Vista. Here's a few of the articles from Microsoft's site. http://support.microsoft.com/search/default.aspx?query=%22memory+leak%22&catalog=LCID%3D1033&spid=&qryWt=&mode=r&cus=False
I've been building and supporting Windows infrastructures since Windows 2.0 days and I can tell you that Windows most certainly does have this problem. There are plenty of articles about memory leaks for every version of Windows. Here's a Google list,
Windows 3.11 http://www.google.com/search?hl=en&q=%22windows+3.11%22+%22memory+leak%22
Windows 95 http://www.google.com/search?hl=en&q=%22windows+95%22+%22memory+leak%22
Windows 98 http://www.google.com/search?hl=en&q=%22windows+98%22+%22memory+leak%22
Windows ME http://www.google.com/search?hl=en&q=%22windows+me%22+%22memory+leak%22
Windows XP http://www.google.com/search?hl=en&q=%22windows+xp%22+%22memory+leak%22
Windows 2000 http://www.google.com/search?hl=en&q=%22windows+2000%22+%22memory+leak%22
Windows 2003 http://www.google.com/search?hl=en&q=%22windows+2003%22+%22memory+leak%22
Windows Vista http://www.google.com/search?hl=en&q=%22windows+vista%22+%22memory+leak%22
Or, you can go right to the source at the MS knowledgebase.
Windows 3.11 http://search.microsoft.com/results.aspx?q=%22windows+3%22+%22memory+leak%22
Windows 95 http://search.microsoft.com/results.aspx?mkt=en-US&setlang=en-US&q=%22windows+95%22+%22memory+leak%22
Windows 98 http://search.microsoft.com/results.aspx?q=%22windows+98%22+%22memory+leak%22
Windows ME http://search.microsoft.com/results.aspx?q=%22windows+me%22+%22memory+leak%22
Windows XP http://search.microsoft.com/results.aspx?q=%22windows+xp%22+%22memory+leak%22
Windows 2000 http://search.microsoft.com/results.aspx?q=%22windows+2000%22+%22memory+leak%22
Windows 2003 http://search.microsoft.com/results.aspx?q=%22windows+2003%22+%22memory+leak%22
Windows Vista http://search.microsoft.com/results.aspx?q=%22windows+vista%22+%22memory+leak%22
Although Linux experiences memory leaks, too, the benefit of using an open source operating system is that the operating system and applications can be patched much more quickly than Microsoft tends to patch.
There are similar articles about memory leaks in Linux, http://www.google.com/search?hl=en&q=linux+%22memory+leak%22 but I would not characterize the issue as a "bad problem." My first distro was Slackware back in the mid-90's. I'm currently running a couple versions of Knoppix and a couple of Ubuntu/Edubuntu. In my experience, I haven't seen any significant issues with memory leaks.
In fact, the Linux kernel tends to be much more efficient than other PC-based operating systems.
Because it is stable, fast, and works quite well, many top tier companies are using it to run some of their significant systems. To name just a small few,
Google http://www.infoworld.com/article/02/08/13/020813hnbrin_1.html
Yahoo http://news.yahoo.com/s/nf/20070322/bs_nf/50932
Cisco http://www.linuxworld.com.au/index.php/id;1394751021;fp;4;fpid;3
Boeing http://mtechit.com/linux-biz/aerospace_industry/boeing.html
DaimlerChrysler http://mtechit.com/linux-biz/automotive_industry/daimlerchrysler.html
Mercedes Benz http://mtechit.com/linux-biz/automotive_industry/mercedes.html
Netscape http://mtechit.com/linux-biz/internet_companies/netscape.html
Top service providers are also supporting customers with Linux.
IBM http://www-03.ibm.com/linux/
Dell http://www.dell.com/content/topics/global.aspx/alliances/en/linux?c=us&cs=555&l=en&s=biz
An independent industry watchdog predicts that Linux desktop sales will hit 10 Billion dollars in 2008. http://news.com.com/IDC+Linux+PC+sales+to+hit+10+billion+in+2008/2100-7344_3-5492399.html
All of this is happening because Linux is a viable, alternate operating system. The complexity of an operating system, the variations of hardware that it may run on, and the interactions of cross-functional applications make it nearly impossible to have an OS that works flawlessly. Linux runs well, and many would say that it runs better, faster, more efficiently, and with quicker patching than any MS offering.