Resolution

Resolution is measured in dots per inch (DPI), which is how many individual dots a printer can print next to each other on a line one inch long. This is, however just one of the factors that decides how good a printers output is. Most printer manufacturers today employ many picture enhancement routines and offer "photo-cartridges" with more colours of ink to improve print quality. However, the general rule of thumb that higher resolution means better quality still holds true. Epson has a series of printers that print at a very high 1440 dpi, but be aware that printing at such a resolution is a very slow process and that you will want to use expensive high quality paper to get the most out of such printers.
It's also important not to ignore other factors of a printers usability, such as speed, build quality, noise level and running costs.

The right paper

So you've just bought a 13000 colour inkjet printer. The last thing you then want to do is feed it with standard paper as then you might as well just have bought a 6500 printer. To print at high resolutions with good colours, you should invest in special coated paper or even the very expensive glossy paper. It is often possible to find packs that include a few sheets of 3-5 types of paper, which you can then test-print on to find out which type of paper is best for your needs. To an extent, the printer companies are guilty of making people believe they can use normal paper, as they advertise this as being a feature of each new printer. However, no amount of printing technology is going to make low quality paper produce as good prints as high quality paper.

Speed

The speed of a printer is given in pages per minute or sometimes for slow colour printers, minutes per page. Take the numbers advertised by the manufacturers with a pinch of salt as they are invariably measured with the printer printing at a low resolution and thus don't show how fast it is at printing at high quality.

Good inkjet printers:

Hewlett Packard have the best reputation for build quality and provide good print quality to boot.
Epson printers provide the ultimate in print quality at a good price point. There are however some doubts about build quality and speed. But if it's high quality output you want, this is it.
No matter which brand of inkjet you go for, I would recommend that you don't buy the cheapest model in the range - moving up to the second cheapest often brings very worthwhile improvements.

Bad inkjet printers:

While I wouldn't call them bad, we have become somewhat disillusioned with Canons series of printers. Their build quality is dubious, often leading to having to replace the print heads (which is expensive) and their price level doesn't give them any great advantage over Hewlett Packard and Epson.