Being 25+ pounds overweight during my entire running career, loose shorts are impractical (the moving fabric facilitates chafing) and tight shorts make me feel self-conscious. The solution for hot days? Running skirts! They have tight/compression shorts underneath, and a looser skirt on top to hide said compression shorts. It is an extra layer of fabric, but overall I've found it to be a comfortable option for all but the most extreme summer heat.
My favorite running skirts are the Lucy Endurance (the overlapping front/back instead of a continuous skirt makes sure it doesn't inhibit movement) and the Brooks PR Mesh Skort II (the gripping on the shorts hem prevents them from riding up, but it lacks a drawstring for a well-fitting waistband).
I don't really have a standard running tank top. The one pictured above is a North Face tank I got at REI. I also have some by Lucy, Patagonia, Brooks. As long as it's tech fabric, it works.
Fall & Spring
I do have a standard t-shirt: Target C9 by Champion. Less than $10 and ridiculously comfy. Depending on how chilly it is, I often start a run wearing arm-warmers (they're from Brooks last year but I can't find them on the website now).
On the bottom for in-between weather, I have a couple pairs of Lucy Endurance capris. They're tight without being overly-compressiony, and have a drawstring in the waistband for the perfect fit. There's also a zippered pocket on the back of the waistband (the above mentioned skirts have this as well) to hold a house key or pack of ShotBloks.
(The sparkle skirt isn't typical winter running attire - this pic was before a New Year's run at midnight last year.)
By about 45 degrees I'll add gloves and a headband to keep my ears warm.
By 35 degrees, I need long pants on the bottom. I'm uncomfortable with the typical "running tights" that are compression and taper to your ankle; so far I've just gone with basic tech-fabric yoga-type pants (also Target C9 by Champion). It lacks the zippered pocket, but works just fine otherwise.