She cant change those things, why worry ? Yes she may die when an asteroid hits the earth, she may be dead already. She cant do anything about it, so why worry ? If it happens it happens.
Death is the same.

So is the cancer one to a degree, you may get it for no reason, you can limit it by not smoking, drinking and other minor stuf. But not much to worry about becuase you can still get it even if you avoid those things. Worrying changs nothing, only makes it worse when your healthy.

As for low self esteem, im in the same boat so have no real advise for that.

I dont know why you wouldnt talk to people about them. Your on the internet, unless you link somethinglike FB, or are speaking to a really determined stalker, no one knows who you are. You could always find somepone, there are even forums for psychological things tto talk about e.g anxiety. Im sure you can find one for phobias, or just talk to people in general, again most people have no idea who you are.

Take her to a phychiatrist, or whoever deals with mental illnesses, self diagnosing is rather foolish since its never fully known if you're/she's 100% correct and she'll never get the proper treatment and just cause more injury through stress and other related injuries.
Kosmikophobia, just dont have her watch Starship Troopers or War of The Worlds and keep the news/Discovery Channels off when they say something about space/NASA is coming on.
Carcinophobia, isn't everyone to a degree afraid of getting cancer, comfort her and tell her its a feeling everyone shares and she should stress about it when she doesn't have it.
Really a trained person should be dealling with her and diagonsing her appropriately.

So your girlfriend has an irrational fear of being alive....And dying.

Phobia - You keep using this word, I don't think it means what you think it means.

This thread makes me wonder how severe a fear has to be so that it can be considered a phobia, I made this thread a while back...

http://www.gamesas.com/index.php?/topic/1216808-me-my-friend-and-his-dog

... and I'm not even sure if I could classify myself as having a phobia. I'm quite certain the way I react to dogs isn't really normal but a phobia ? Not so sure at all...

Anyway as for her self esteem if you want to help her with that don't tell her she's great, give her opportunities to show you that she is great and hope that she can follow through on them. I myself was always very confident in myself as I was quite accomplished in just about anything as a child, but when I grew into my teenage years I found myself becoming a bit of a social outcast due to my narcissistic nature (yeah, looking down on your peers isn't a great way to make or keep friends...) and I started to lose confidence in myself and started to be pretty lonely hanging out with myself and I started to blame my failings on myself (well it's true that they were my fault but there is a certain line you shouldn't cross when beating yourself up mentally).

Not long after I started to be more of a loner I started playing the online game World of Warcraft, it felt pretty great, a clean slate where no one has any preconceptions about you, but that didn't change that I didn't feel very confident in myself when it came to social situations anymore and I kept to myself pretty much even within the game and tried my best just to be polite and invisible. However one day after being in a guild for some time one of the officers of the guild recognized that I was generally just helpful and didn't partake in arguments much and I was asked if I wanted to be an officer of the guild. This lead to me trying to do my best as an officer and gradually as I worked harder to moderate the guild and keep trouble down in it I started rising in ranks until one day for reasons irrelevant to this thread there was a need to appoint a new guild master.

At this point I was fully expecting that the officer that had ranked me up would take the place but through a general vote of the guild I was chosen instead. A huge confident booster when you get pit up against someone who you think does a good job at something and then a bunch of people vote for you over said person. No matter how "unreal" some people may look at social interactions in WoW it is still real people sitting at the other end of their avatars at the end of the day, people with thoughts and opinions. Recognition for doing something well from people who some don't have any close ties to you is really a big confidence booster, far bigger than simple words of comfort from those you already know will shower you with praise no matter what.

So don't just tell her "you're great" or "it's okay to fail" or anything that show you pity her and feel like you need to comfort her, there is no confidence to be found in that. If you can put her in a position where she has to do something and where she is likely to get praise if she does it well, and even better if it's from people you don't know already. Like does she sing well ? Perhaps you'd like to take her out for karaoke, is she an aspiring actor ? Perhaps you'd like to push her to give that a try, or perhaps she is a great baker and X-mas just happens to be coming around, there must be some bazaars to sell baked goods or something of the sort...

Well my ideas may be bad but don't let that stop you from having your own good ideas about how to instill confidence through tasks, not words.

I don't know the person to comment on whether they're really phobias, but generally the whole point is that they're irrational, so just telling someone they don't make sense isn't going to accomplish much.

I have Hipsterphobia... Get away from me!

To save anyone else googling:

Atychiphobia - fear of failure
Carcinophobia - fear of cancer
Kosmikophobia - fear of cosmic phenomena
Obesophobia - fear of becoming overweight
Thanatophobia - fear of death

To the OP- are you sure these are actual genuine 'phobias' or is she just anxious about them? I'd say fear of failure is probably an anxiety more than an actual fear, for example. I'm not trying to belittle her problems, but turning them into something bigger than they are ("making mountains out of molehills" as my mother used to say) won't help her get over them any easier. I get a little anxious in enclosed spaces like lifts and aeroplanes, but I wouldn't describe it as a 'phobia'.

There isn't much you can do about cosmic phenomena I'm afraid, but fear of being overweight you can help with, if you're worried about her developing an eating disorder. You're probably in the US but take a look at this anyway, there's some good advice there- http://www.bbc.co.uk/health/emotional_health/mental_health/mind_eatingdisorders.shtml
Otherwise, being supportive and understanding is the best way to go about this. You won't be able to cure her fear of cancer/death, but you can be there for her and help her relax a little about it.