The biggest suicide crisis network in the US is 1-800-273-8255 (273-TALK), the NationalLifeline. They are a combination of several national programs. When you call, you are routed to an affiliate crisis center nearest to your area code.
With cell phones being common now, this means that sometimes you'll get routed to the crisis center nearest your cell area code, which may or may not be near where you actually are.
Some regions have better training than others. Volunteer staffing with supervision; the supervisors are always good, and there should always be one. You can't really say 'let me talk to your supervisor', but you can ask if there's anyone else you can be transferred to. Their crisis chat is excellent; but it's not 24/7, and can be hard to get through.
http://www.suicidepreventionlifeline.org/gethelp/lifelinechat.aspx
Link Removed Is another resource; they are affiliates of the National Lifeline, above, but can also be reached directly. They also have online crisis chat. They have a few numbers but the easiest to remember is 1-800-442-HOPE. Volunteer staffing with excellent supervision and training.
Dead Link Removed - the Samaritans in NY don't have a 1-800 number, so they aren't toll-free, but they are available. Volunteer staffing, decent supervision.
http://www.boystown.org/hotline The Boys Town crisis line 1-800-448-3000 is a staffed 24-hour line. They emphasize counseling for children, teens, and young adults - but I've never heard of anyone being turned away for being too old. I'd be curious to know if that's ever happened to anyone, here. They are very well trained. They also have a crisis chat line. Their other name is YourLifeYourVoice.
Depending on where you are, you may be near a crisis center being managed by a graduate program in social work or psychology; it's worth really researching your local options, to know what's there and what's not there.