Good topic. 1998 was a good year for me, being at university (foundation art course - well slacker), making new friends and going out a lot. Strangely though I don't think I was listening to a lot of new music, but there was still a lot of good stuff. So, a few from that year would be:

Garbage: Version 2.0 (also saw them live for the first time that year - not sure I love the record itself so much now, production wise, but great songs anyway)
Sparklehorse: Good Morning Spider (started getting introduced to stuff like this around this time - what a guy - RIP)
Mogwai: Kicking a Dead Pig (plus the No Education = No Future EP came out that year)
Arab Strap: Philophobia (seem to remember seeing them live that year too - if I had a time machine...)
Skinny Puppy: Remix Dystemper (perfect for those of us still discovering old industrial music, but into contemporary dance music too)
PJ Harvey: Is This Desire? (still a favourite - I'd loved to have seen her around this time)
Depeche Mode: The Singles 86/98 (a best of shouldn't count, but I fucking love my vinyl box of this, plus Only When I Lose Myself was a top single)
Lo Fidelity Allstars: How To Operate With A Blown Mind (bet nobody else comes up with that one)

Placebo, Smashing Pumpkins and Massive Attack have been mentioned. I didn't have these albums, but I was listening to the singles for sure. Good stuff. Did somebody mention The Jon Spencer Blues Explosion too? I really enjoy that now, but kind of missed it at the time.

Another album I didn't have from '98 is Fatboy Slim's You've Come A Long Way, Baby. The Rockafeller Skank was released in June '98 (says Wikipedia) so it sounds right to say that was the hit of the summer, and therefore the year. It probably got really annoying at the time, but looking back it makes me feel warm and fuzzy.

Thinking more generally about what I was listening to in '98, I have to mention a couple from the previous year that were still getting a lot of play:
Pigface: A New High In Low
Recoil: Unsound Methods (might be dated, but still highly recommended)
Radiohead: OK Computer (SO bored of it now, but at the time it was HUGE, and everyone was just well into Radiohead)

And as we're moving around in time, I have to mention The Creatures and Moby who both released singles in '98 from albums that would come out the following year. Play may be very uncool now (in fact it wasn't very cool at the time either) but Honey was a good single, and I'm sure I heard a couple of other songs before the end of the year. 2nd Floor was a great first single from Anima Animus - the green 7" remains very much loved.