A while ago, I bought a 1982 Ibanez Roadstar bass on something of an impulse. It played so well and felt so good (and was cheap - around £330) I had to have it. I'm glad I did, as it's now probably my favourite bass out of all the ones I own, including vintage Fenders worth three times the price.
Here's what it looked and sounded like pre modification.
And here it is in all it's glory!
A couple of important points:
You may be interested in this video I made about building a P bass from scratch (and what parts are commonly modified on bass guitars). My Ibanez proves that a bass that plays like a dream does not have to break the bank.