I have a ceiling mounted Hampton Bay product with one T3 halogen bulb and four spots. I cannot remove the burned out T3 to replace it. Any suggestions?

Be sure the power is off, spray a bit of WD40 into the socket threads, use a pair of needle nose pliers, insert into inner base of lamp. Clean out any loose glass first to get deeper into the base metal. Spread the plier handle so the tips of the needle nose dig in, and firmly turn the pliers as you grip the inside of the base.

Next time, put a little vasalene on the threads when you install the new lamps.

Damn I get a reddie, now what do I do? Hang my head in shame, I missed a light bulb, better stick to code.

A T3 lamp will push to one side or the other.

I have a ceiling mounted Hampton Bay product with one T3 halogen bulb and four spots. I cannot remove the burned out T3 to replace it. Any suggestions?
... use a rag to cover the bulb, it may break you, and follow the new bulb's instruction; make sure you wipe it clean after installation

Rather than break the bulb as suggested in an earlier answer, try this first: spray both ends with the lubricant, let sit for a minuted and then very carefully rotate each end with a pair of pliers to break the seal. One-eight of a turn or less should do it. You may dislodge the glass from the ceramic end piece but it shouldn't break into pieces. Then use the pliers to pull one end toward the other end until it clears the edge and then pull it toward you and out. (This approach is the only feasible way to deal with a protective tube in some European fixtures)