Firstly, I think it's important that you noted that nothing lasts forever. The PS2 has components that will eventually wear out over time, even if preserved or used sparingly.
Most notably, it is likely that one or all of these components will eventually fail:
- Controllers - Obviously wear & tear use but also the rubber domes that provide both the button 'depress' and spring-back can eventually wear out.
- Memory Cards - Memory cards are built on a type of Flash memory that - like all flash memory - has limited reads and writes. Eventually they will also fail.
- Power supply - Capacitors wear out over time, even when not used
- Disk drive - Spin motor can burn out and/or rubber and plastic components can become brittle and break with age or rapid heat/cool cycles.
- This includes the Clamshell lid or disk drive tray (depending on whether you have a slim or phat PS2), either way plastic clips or the parts that control ejecting DVDs will wear out.
This isn't an exhaustive list of what can break but they will be the most common complaints of broken hardware. Note that if any of these happen to you that all hope is not lost, most of these parts are replaceable, and there are third-party (i.e. not Sony) vendors that still offer replacement parts (and will for years to come).
Now, in terms of your actual question of how to look after your PS2 so that it will have a long lifetime, it's all the simple stuff really:
- Make sure it has a lot of ventilation in a dust-free environment
- Don't play it in areas of excessive heat or humidity (don't play during heat waves or humid days unless you have air conditioning keeping everything cool and dry),
- Keep it away from sources of heat (like fireplaces or heaters)
- Don't leave it on 'idling' or 'paused' for extended periods of time.
- Don't set it up somewhere where it's likely to be knocked off (or pulled off by someone tripping over a cable) - avoid 'hard shocks'
- Don't throw your controller across the room when you're losing.
- Put your disks back in their case when you're done playing.
- Pack everything away when you're done - don't leave controllers around where someone can step/trip on them.