It looks like a Yucca plant (not sure of botanical name). It definitely appears to be in need of repotting and a drink!
If the leaves are dull and dirty, give them a clean with some warm water and a cloth. I find cotton wool works as loo roll leaves pieces stuck to the leaves.
Check over for any pest and treat accordingly. the brown leaf tips have probably appeared due to being in a dry but warm atmosphere and so it would be worth misting it occasionally especially as in winter time, temperatures in houses are not at all favourable for plants.
keep it somewhere light and away form radiators, other heat sources and cold drafts.

It should soon pick itself up, the leaves will become greener looking and hopeful do well!

Thanks Nicky, I think I can do all you ask.Fingers crossed.

O, and dont put it into too big a pot, just the next size up as plants aren't growing much at the mo. Use fresh compost and don't compact it or else this seems to make the compost go stale and manky!

Good luck!

Do you think that this plant just needs 'one size up' Nicky. It looks horribly pot bound to me. If just the next size up now, then repot again in spring.

Mmmm, i agree Bulbaholic, it needs a pot that's about 2' tall and diameter .... it's far too big for anything smaller.
The poor thing's screaming for more leg-room :-(

Possibly a Draceana rather than a Yucca though look similar.

The watering regime needs to be adhered to also. Let it dry out between waterings but when you do water, give it a good drink. In winter, the gap between watering can be longer, say three weeks to a month with fortnightly waterings in summer.

Yes this looks more like Dracaena fragrans - definitely needs a much bigger pot. It's lower leaves will yellow and fall off naturally - that happens as it grows. Do as Fractal says with the watering - they need to dry out between drinks ... they don't like wet feet.