Choosing the right tripod will have a dramatic effect on your images! The wrong tripod will give you camera shake even in moderate conditions.
When do you need a tripod? You will need a tripod whenever you are taking pictures that you cannot sucessfully handhold. This is normally when your shutter speed needs to drop below 1/60th of a second. So for all of your movement or long exposure images, eg Sunrise / Sunset, Motion Blur, etc. OR when you are taking high quality Macro shots, you need a good tripod.
Remember that the purpose of a tripod is to keep your camera rock steady during the exposure! If your tripod is not strong enough, it will shake under the stress of, either the wieght of your camera, or in windy conditions. There is nothing worse that doing all the right things, in terms of setup and taking the image, just to end up with a shaky picture because your tripod is not strong enough.
When choosing a tripod, you should extend all 3 legs as far as they go (not the central column), and give them, what I call, the twist test. This means holding onto 2 legs and twisting them laterally. If they flex more than 2-3cms the tripod is not strong enough, and will not perfom in less than ideal conditions.
In terms of models, the minimum standard for a good tripod is the Manfrotto 190B series. There are a few models in this series, and they are all adequate. Prices range from $180 ish to $350 ish depending on where you buy, but go and test one in a good camera store first. If this it too expensive for you, then you need to find another brand that is just as strong. Give them the twist test before buying!
If you need a tripod for travelling, then the best option is to buy the Carbon Fibre Manfrotto, or equivalent, but these are very expensive, starting from around $600. A great alternative is to buy the Fotopro M-5 Mini tripod. This is small, very lighweight and very strong. Weighs around 1.5kg and is very compact for travelling. I recently did a trip to Taiwan and it was amazing for my shots of waterfalls which required a longer shutter speed.The cost is about $130 on ebay so very affordable.