AKA. "I can't afford to buy cheap". I also think that bed mattresses are worth investing in, since you spend 1/3 - 1/4 of your life in it, and being well-rested helps in being productive.
I really get that sentiment—there are an awful lot of ways to be penny wise and pound foolish in this world. You can go through a lot of $150/pr "dress shoes" before you even need to resole a good pair, for instance, and if you need to be dressed up (for work or even for frequent meetings) you can go broke saving money. And trying to save money on your tools (and for a full-time coder, even a chair is a tool) is going to cost you in productivity over the long haul.
On the other hand, I've found that there's nothing better for my back (or my sleep in general) than a properly-inflated air bed (and I had severe back problems for years). (It started as an interim solution when I beat my furniture to a working location by nearly a week.) That works out to about $30 per annum around these parts, and although there are "real" versions with long-term guarantees and fancy fabric coverings (a standard mattress pad gives the same feel) the price differential isn't an incentive to give up the "replace annually" variety.
On the other hand, don't discount cheap ones simply because they are cheap.
I got my old memory foam mattress from Woot. It made me sleep so soundly that after a couple years, I started waking up with back pain. Slept all night, but woke up in pain. Gave it to my Mom (best sleep she's ever had, too) and bought a hybrid from Ikea. Still way better than any other boxspring mattress I've owned, and ridiculously cheap.
So yes, they are worth investing in... But that doesn't mean you have to pay a lot.
Sadly, I cannot find an Ikea chair/couch that's comfortable. Still working on that purchase.