Not much, I'm afraid. The squeak is usually caused by one of two things: either the cassette mechanism is wearing out, or the lubricant on the tape is drying out.
If it's the first case, then you can try opening the cassette up and transferring the tape spools to a cassette shell taken from a tape you don't want any more. If you do decide to try this, pay very close attention to the way the tape is laced around the various rollers and brushes in the cassette, and DON'T touch the tape itself with your bare hands!
If the problem is the lubricant, then you're stuck with it. Literally :-( The lubricant is essential to prevent damage to both tape and machine when playing - if the problem worsens then the tape is likely to get chewed up by the machine, at which point you're looking at having to open your VCR up to get the tape out, plus the risk of damage to the delicate video heads.
The root of this problem is simply that VHS tape stock these days is very poor quality - this is why it's so cheap. Tapes manufactured 20+ years ago are much much heavier than their modern equivalents; this is because the older tape and cassette shell are made from better quality materials. They are also less prone to dropouts and deliver a much better picture. OTOH, tapes that old are also likely to have dried out by now :-(
Your best bet is to replace with DVDs