Mine was a (second-hand) Commodore Plus/4 in 1988, for my 9th birthday. It conked out two days later and it took a while to get it fixed.
It was a good little system: 64K RAM, 128-colour graphics, tape drive, disk drive and a printer, plus a programming manual and a shedload of games. The major downside was that nobody else had one and it was pretty hard to find software; bargain bins in small computer shops and boot fairs (not sure what they're called in the US!) were the places to look. My friends all had other computers: a mix of BBC micros (for the posh kids), ZX Spectrums and C64s (for everyone else) and even the odd Amiga.
I owe a lot to that Plus/4 - it had a primitive word processor, database and spreadsheet in ROM, so introduced me to office software. It of course had BASIC and I was able to dabble with code, although it was more of the "guess the number and win points" type of game rather than anything sophisticated.
That system lasted me for 3 years, by which time my dad rescued an old IBM XT from his work (they'd chucked it into a skip). That gave me an interest in PCs and I've never looked back!