In today's world, travel safety is on everyone's mind. However, LGBTI travelers need to take additional issues into consideration when on the road, including social attitudes, legislation, policies, and healthcare relevant to lesbian, gay, bisexual, transgender, and intersex individuals. There is an increasing amount of information available and I found the following very helpful:
ManAboutWorld publishes the Guide to Travel Safety
Spartacus International Gay Guide publishes the Gay Travel Index
US State Department has a page with LGBTI Travel Information, including links to numerous other sources.