Personally, I'm a fan of High Deduct. plans. I've been on one since 2001 and find it great.
The key is to fund the account your first year in. Most employers at least partially fund it for you and if not, get it funded. Then if anything happens, depending on your plan, you're covered.
Case in point, if my son breaks his leg, wife a hip, etc. I'm responsible on our plan for the first $2,500. for the next 7,500 I pay 10%, once we're at $10k in bills I'm covered at 100%. Our family max out of pocket is $4,500 Thus for the first very bad incident, I'm going to pay $3,250 out of my pocket and then if another bad thing happens, I'll pay another $1,250 at which our plan is fully funded and we're all covered at 100%.
The rest is pure savings for time ahead including when the wife an I are old and gray. By "the rest" I mean the $453 +/- I put into my HSA each month that no one can take away. On the old style plans I paid that money and it was a pure waste. Money I would never see coming back to me.