You can upgrade, but not to anything really good.
The Acer Aspire X1900 isn't a regular full-sized desktop, it's a compact small-form-factor PC. It can only accept low-profile graphics cards, standard full-height cards won't fit inside the case.
The X1900 also has a weak 220 watt power supply, which restricts your choices even further. You can't support the best low-profile cards (which require at least a 300 watt power supply), you can only use models which have a low power draw.
The best cards you can install in that computer are the GeForce GT 520 or Radeon HD 6450, which are roughly $45 models. Anything better requires too much power.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814130632
http://www.newegg.com/Product/Product.aspx?Item=N82E16814127584
Between them the GT 520 is slightly better. While they're low-end cards which aren't really designed for gaming, they're a big improvement from your integrated GMA X4500. They could play games like Rift, CoD and WoW well on medium settings at resolutions of 1600x900 or less.
Your current integrated graphics are slower than the bottom card on this chart, while the GT 520 is basically an updated GT 220... it has the same performance.
http://www.techspot.com/review/244-ati-radeon-hd-5450/page7.html
Here's a more current comparison, with slightly better cards:
http://www.techpowerup.com/reviews/Zotac/GeForce_GT_520/9.html
The power supplies in slimline/small form factor PCs are proprietary, not standard sized. So you can't simply order a higher-wattage PSU from Amazon or Newegg- only PSUs made specifically for your computer model will fit. And unfortunately it doesn't appear that anything better exists for that particular unit.
http://support.acer.com/acerpanam/desktop/2010/acer/aspire/AspireX1900/AspireX1900sp2.shtml